# Lesson Worksheet: The Pythagorean Theorem Mathematics • 8th Grade

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.

Q1:

Find in the right triangle shown. Q2:

Find the area of the triangle , correct to one decimal place. Q3:

Given that the triangle is right-angled at , , and , find the length of .

Q4:

Determine the length of the longest side of a right triangle if the lengths of the two other sides are 6 cm and 8 cm.

Q5:

Which of the relations below is correct? • A
• B
• C
• D

Q6:

Given that is a right triangle, where and , determine the length of . Q7:

Find in the right triangle shown. Q8:

Find in the right triangle shown. Q9:

is a right 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.

Q11:

Determine, to the nearest tenth, the perimeter of a right triangle, given that its hypotenuse is 49 cm and that one of its sides is 26 cm.

Q12:

Given that is a square, find the length of . 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 triangle, which of the following is equal to the area of the square that has the hypotenuse as a side?

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

• A
• B3
• C
• D2
• E1