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Lesson: The Pythagorean Theorem

Sample Question Videos

Worksheet • 25 Questions • 6 Videos

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 𝐴 𝐡 𝐢 is right-angled at 𝐡 , 𝐴 𝐡 = 1 2 c m , and 𝐡 𝐢 = 5 c m , find the length of 𝐴 𝐢 .

Q4:

Given that the triangle 𝐴 𝐡 𝐢 is right-angled at 𝐡 , 𝐴 𝐡 = 1 2 c m , and 𝐡 𝐢 = 1 6 c m , find the length of 𝐴 𝐢 .

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.

  • A √ 2
  • B3
  • C2
  • D √ 3
  • E1

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:

𝐴 𝐡 𝐢 is a right-angled triangle at 𝐡 , where 𝐴 𝐡 = 1 2 6 c m and 𝐡 𝐢 = 7 8 . 4 c m . Find the length of 𝐴 𝐢 .

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

Is the triangle a right triangle?

  • Ano
  • Byes
  • CIt is impossible to tell.

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