# Worksheet: The Pythagorean Theorem

In this worksheet, we will practice using the Pythagorean theorem to find the length of the hypotenuse or a leg of a right triangle and its area.

**Q8: **

Find in the right triangle shown.

**Q9: **

is a right-angled triangle at , where and . Find the length of .

**Q10: **

Determine the diagonal length of the rectangle whose length is 48 cm, and width is 20 cm.

**Q13: **

Determine the area of .

**Q14: **

Find in the right triangle shown.

**Q15: **

Find in the right triangle shown.

**Q16: **

Find in the right triangle shown.

**Q17: **

Find in the right triangle shown.

**Q18: **

Find in the right triangle shown.

**Q19: **

Find in the right triangle shown.

**Q20: **

Find in the right triangle shown.

**Q21: **

In a right-angled triangle, which of the following is equal to the area of the square that has the hypotenuse as a side?

- AThe area of the square drawn on one of the other two sides.
- BThe sum of the perimeters of the squares drawn on the other two sides.
- CThe sum of the areas of the squares drawn on the other two sides.

**Q22: **

Find in the right triangle shown.

**Q23: **

A triangle has vertices at the points and .

Work out the lengths of the sides of the triangle. Give your answers as surds in their simplest form.

- A and
- B and
- C and
- D and
- E and

Is the triangle a right triangle?

- Ayes
- BIt is impossible to tell.
- Cno

**Q24: **

Find in the right triangle shown.

**Q25: **

Find the length of the hypotenuse of a right triangle whose leg lengths are 1.

- A1
- B2
- C
- D
- E3