In right-angled triangle PQR, Q^​=90∘, PQ = 8 cm and QR = 15 cm. Find the length of the hypotenuse PR.

The hypotenuse of a right-angled triangle is 25 cm. If one of the other sides is 7 cm, find the length of the third side.

Which of the following is a Pythagorean triple? (a) (6, 8, 9) (b) (5, 12, 13) (c) (7, 20, 21)

A 10 m ladder leans against a vertical wall. Its foot is 6 m away from the base of the wall. How high up the wall does the ladder reach?

In triangle ABC, the lengths of the sides are 9 cm, 12 cm, and 15 cm. Show that it is a right-angled triangle.

The diagonals of a rhombus are 16 cm and 30 cm long. Find the perimeter of the rhombus.

In rectangle ABCD, AB = 12 cm and BC = 5 cm. Find the length of the diagonal AC.

In an isosceles triangle ABC, AB = AC = 17 cm. The altitude from A to BC is 15 cm. Find the length of BC.

Prove that in a square with side length 'a', the length of the diagonal is .

A ship sails 12 km North and then 35 km East. What is the shortest distance from its starting point?

In triangle ABC, AD is the altitude to BC. If AB² = AD² + BD², what is the magnitude of angle AD^B?

A man goes 150 m east and then 200 m north. Find his distance from the starting point.

In triangle ABC, AB^C=90∘. P is the midpoint of BC. Prove that AP2=AC2−43​BC2.

Using Euclid's formula for Pythagorean triples with x=4,y=3, generate the triple.

A utility pole is supported by a wire which is attached from a point 1 m below the top of the pole to a point on the ground 8 m from the foot of the pole. If the pole is 7 m high, find the length of the wire.