The Baudhayana-Pythagoras Theorem

If a square has side 7 m, the area of the square that doubles it is:

Which ancient Indian text contains the earliest statement of the theorem used to double a square?

If the area of a square is 50 sq cm, what is the length of its side?

What is the area of a square with a diagonal of length $\sqrt{18}$ units?

The diagonal of a square $S$ is equal to the side of square $T$. If the area of square $S$ is 12, what is the area of square $T$?

If the side of a square is $x+1$, what is the area of the square that 'doubles' it?

A square field has an area of 200 m$^2$. A path is to be made along its diagonal. What is the length of this path?

A square tile has a diagonal of length $k$. If we need to cover a floor area that is exactly $8$ times the area of this tile using a single large square slab, what must be the side length of that slab?

An architect is designing a square plaza. The inner zone is a square of side $s$. The outer zone is a square walk-way such that the total area (inner zone + walk-way) is exactly double the inner zone. If the diagonal of the total plaza is $20$ meters, find the area of the inner zone.

Given a square with side $a$, a second square is constructed on its diagonal. A third square is then constructed such that its area is the sum of the areas of the first two squares. What is the side length of the third square in terms of $a$?

Which of the following values represents the diagonal of a square with side $5$ units?

A right-angled triangle is formed by halving a square of side $a$. What is the length of the hypotenuse?

What is the ratio of the side of a square to its diagonal?

If the side of a square is increased from $x$ to $x\sqrt{2}$, how does the area change?

If the square of the diagonal of a square is $100$ sq units, what is the area of the square?

If the side of a square is doubled, by what factor does the length of its diagonal increase?

In a square $PQRS$, diagonal $PR = 4$ cm. What is the area of $\triangle PQR$?

A square tile is halved by joining midpoints of adjacent sides to form a smaller square. If the diagonal of the smaller square is $10 \text{ cm}$, what was the area of the original larger tile?

A large square has an area of $S$. A sequence of squares is formed such that each subsequent square's vertices are the midpoints of the previous square. If the sum of the areas of the first three squares in this sequence is $175 \text{ cm}^2$, find the side length of the first square.

In a square $ABCD$ with side $10 \text{ cm}$, points $E, F, G, H$ are midpoints of $AB, BC, CD, DA$ respectively. If a point $P$ is chosen at random inside square $ABCD$, what is the probability that $P$ lies inside the square $EFGH$?

In an isosceles right triangle, the hypotenuse squared is equal to how many times the square of one of the equal sides?

If the equal sides of an isosceles right triangle are $s$, the area is $\frac{1}{2}s^2$. If $s=2$, find the hypotenuse.

A ladder is leaning against a wall making an angle of $45^\circ$ with the ground. If the foot of the ladder is 3 m away from the wall, how long is the ladder?

In an isosceles right triangle, if the side opposite to the $90^\circ$ angle is $8\sqrt{2}$ cm, what is the length of each of the other two sides?

Find the length of the hypotenuse of an isosceles right triangle if the sum of the squares of all three sides is 100 cm$^2$.

The perimeter of an isosceles right triangle is $2 + \sqrt{2}$ meters. What is the length of its hypotenuse?

If the length of each side of an isosceles right triangle is increased by a factor of $\sqrt{2}$, by what factor does the hypotenuse increase?

A flagpole is secured by a wire that forms an isosceles right triangle with the ground and the pole. If the wire is attached to the ground $6$ meters away from the base of the pole, how long is the wire?

An artist creates a mosaic using small tiles in the shape of isosceles right triangles. If the hypotenuse of each tile is $\sqrt{8}$ cm, what is the length of the equal sides of each tile?

A right isosceles triangle has a perimeter of $10 + 5\sqrt{2}$ cm. What is the length of its hypotenuse?

In a triangle with sides $7, 24,$ and $25$, what type of triangle is it?

If the legs of a right triangle are equal and the hypotenuse is $10\sqrt{2}$ units, what is the length of each leg?

Two squares with side lengths $6$ cm and $8$ cm are combined to form a single larger square. What is the side length of the new square if its area is the sum of the areas of the original two?

A wire is attached to the top of a $15$ m pole and anchored to the ground $8$ m from the base. How long is the wire?

A right triangle has a hypotenuse of $25$ cm. If the ratio of its legs is $3:4$, find the length of the shorter leg.

If the side of an equilateral triangle is $2a$, find its altitude using the Baudhayana-Pythagoras theorem.

What is the area of a square built on the hypotenuse of a right triangle with legs of $8$ cm and $15$ cm?

An artisan is creating a mosaic where a large square tile is formed by the combined area of two smaller square tiles. The side of the first small square tile is $15$ cm. The side of the large square tile is $17$ cm. If the artisan needs to find the perimeter of the second small square tile used in the combination, what is its value?

A city planning committee wants to combine two square-shaped parks, Square $A$ and Square $B$, into a single large square park, Square $C$, such that the area of Square $C$ is exactly the sum of the areas of Square $A$ and Square $B$. Square $A$ has a side length of $12$ m. The total length of the fencing required for Square $B$ is $20$ m. What is the side length of the newly formed Square $C$?

A square sheet of metal has an area equal to the sum of the areas of two square sheets with side lengths $10 \text{ cm}$ and $24 \text{ cm}$. If this larger sheet is then cut into smaller square pieces each of side $2 \text{ cm}$, how many such pieces will be obtained?

The smallest member of a Pythagorean triplet is $8$. Find the other two members.

In a right triangle, the two legs are $15$ m and $20$ m. What is the hypotenuse?

A rectangle has a length of $24$ units and a diagonal of $25$ units. Find its width.

If a square has a side of $7$ cm, what is the length of its diagonal (approximate to nearest integer)?

In a right triangle, the legs are in the ratio $3:4$. If the hypotenuse is $20$ cm, find the length of the shorter leg.

A ship sails $24$ km due North and then $7$ km due West. How far is it from the starting point?

If a Pythagorean triplet is $(14, x, 50)$, what is the value of $x$?

A rhombus has diagonals of lengths $18$ cm and $24$ cm. Find the perimeter of the rhombus.

A room is $12$ m long, $9$ m wide, and $8$ m high. What is the length of the longest rod that can be placed in the room?

In a square-shaped field $ABCD$ of side $21$ m, a path runs diagonally from $A$ to $C$. If a man walks from $A$ to $B$ and then to a point $P$ on $BC$ such that $BP = 20$ m, how much further is he from point $A$ than he would be if he were at point $B$?

If the sides of a triangle are $9\text{ cm}$, $40\text{ cm}$, and $41\text{ cm}$, is it a right-angled triangle?

Which of the following is the correct statement of the Baudhayana-Pythagoras theorem for the triangle shown?

In a right triangle, the two legs are $20\text{ cm}$ and $21\text{ cm}$. What is the hypotenuse?

A rectangle has a length of $12\text{ cm}$ and a diagonal of $13\text{ cm}$. What is its width?

In a circle of radius $10\text{ cm}$, a chord is at a distance of $6\text{ cm}$ from the center. What is the length of the chord?

If the length of the hypotenuse of a right triangle is $x+2$ and the legs are $x$ and $x+1$, find the value of $x$.

A square is inscribed in a circle of radius $5\text{ cm}$. What is the area of the square?

A wire is attached to the top of a 15 m vertical pole and anchored to the ground 8 m from the base. If the wire is then moved to a 20 m pole and anchored such that the length of the wire remains the same, how far from the base of the new pole is the anchor point?

A right triangle has a hypotenuse of length $c = 25$ units and one leg $a = 7$ units. If a new triangle is formed by doubling the length of both legs, what is the length of the new hypotenuse?

A drone flies 8 km North, then 15 km East, and finally 12 km North again. How far is the drone from its starting point in a straight line?

Find the length of the hypotenuse of a right-angled triangle whose other two sides are $12$ cm and $35$ cm.

A $10$ m long ladder reached a window $8$ m high from the ground on placing it against a wall at a distance $a$. Find the value of $a$.

A rectangular swimming pool is $12$ m long and $5$ m wide. What is the distance between two opposite corners of the pool?

A man goes $150$ m due East and then $200$ m due North. How far is he from the starting point?

The perimeter of a right-angled triangle is $30$ cm and its hypotenuse is $13$ cm. Find the lengths of the other two sides.

A rectangle has a width of $9$ cm and a diagonal of $41$ cm. Find its area.

In triangle $ABC$, $AB = AC = 25$ cm and $BC = 14$ cm. Find the altitude from $A$ to $BC$.

In triangle $ABC$, $\angle ABC = 90^\circ$. $D$ is the midpoint of $BC$. Which of the following relations is true based on the Baudhāyana-Pythagoras Theorem?

A traveler starts at $(0,0)$ on a coordinate grid. He travels to $(15, 0)$, then to $(15, 20)$, and finally to $(6, 32)$. What is the shortest distance from his final position back to the starting point?

Two buildings are $60$ meters apart. From a window $15$ meters high in the first building, the distance to a window in the second building is $75$ meters. What are the possible heights of the window in the second building?