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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.

Q1:

Find π‘₯ in the right triangle shown.

Q2:

Find the area of the triangle 𝐴 𝐡 𝐢 , correct to one decimal place.

Q3:

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

  • A 119 cm
  • B 17 cm
  • C 7 cm
  • D 13 cm

Q4:

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

  • A 112 cm
  • B 28 cm
  • C 4 cm
  • D 20 cm

Q5:

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.

Q6:

Determine the length of the longest side of a right triangle if the lengths of the two other sides are 32 cm and 60 cm.

Q7:

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.

Q8:

Given that 𝐴 𝐡 𝐢 𝐷 is a square, find the length of 𝐷 𝐸 .

Q9:

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

  • A1
  • B2
  • C √ 3
  • D √ 2
  • E3

Q10:

Find the length of the hypotenuse of a right triangle whose leg lengths are 3 and 4.

Q11:

Find π‘₯ in the right triangle shown.

Q12:

Find π‘₯ in the right triangle shown.

Q13:

Find π‘₯ in the right triangle shown.

Q14:

Find π‘₯ in the right triangle shown.

Q15:

Find π‘₯ in the right triangle shown.

Q16:

Find π‘₯ in the right triangle shown.

Q17:

Find π‘₯ in the right triangle shown.

Q18:

Find π‘₯ in the right triangle shown.

Q19:

Find π‘₯ in the right triangle shown.

Q20:

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

  • A 14.3 cm
  • B 204.4 cm
  • C 98.6 cm
  • D 148.4 cm

Q21:

A triangle has vertices at the points 𝐴 ( 4 , 1 ) , 𝐡 ( 6 , 2 ) , and 𝐢 ( 2 , 5 ) .

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

  • A 𝐴 𝐡 = 5 , 𝐴 𝐢 = 4 √ 2 , and 𝐡 𝐢 = √ 7
  • B 𝐴 𝐡 = 5 , 𝐴 𝐢 = 5 √ 2 , and 𝐡 𝐢 = 5
  • C 𝐴 𝐡 = √ 5 , 𝐴 𝐢 = 2 √ 3 , and 𝐡 𝐢 = √ 7
  • D 𝐴 𝐡 = √ 5 , 𝐴 𝐢 = 2 √ 5 , and 𝐡 𝐢 = 5
  • E 𝐴 𝐡 = 5 , 𝐴 𝐢 = 5 √ 2 , and 𝐡 𝐢 = √ 5

Is the triangle a right triangle?

  • Ayes
  • BIt is impossible to tell.
  • Cno

Q22:

Find π‘₯ in the right triangle shown.

Q23:

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.

Q24:

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

Q25:

Find π‘₯ in the right triangle shown.

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