Lesson Worksheet: The Pythagorean Theorem Mathematics

In this worksheet, we will practice using the pythagorean theorem to find a missing length in a right triangle and using the converse of the pythagorean theorem to determine whether a triangle is a right triangle.

Q1:

Find 𝑥 in the right triangle shown.

Q2:

Find 𝑥 in the right triangle shown.

Q3:

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.

Q4:

Given that the triangle 𝐴𝐵𝐶 is right-angled at 𝐵, 𝐴𝐵=12cm, and 𝐵𝐶=5cm, find the length of 𝐴𝐶.

Q5:

Find the perimeter of 𝐴𝐵𝐶𝐷.

Q6:

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

Q7:

Which of the relations below is correct?

  • A49=𝑥+16
  • B𝑥=4+7
  • C7=𝑥16
  • D𝑥=(7+4)

Q8:

Find the length of 𝐷𝐶 in the trapezoid 𝐴𝐵𝐶𝐷.

Q9:

𝐴𝐵𝐶 is a right triangle at 𝐵, where 𝐴𝐵=36cm and 𝐵𝐶=46cm. Find the length of 𝐴𝐶 giving the answer to three decimal places.

Q10:

In the figure, if 𝐶𝐷=19cm, determine 𝐵𝐷 and 𝐴𝐶 to the nearest hundredth, if necessary.

  • A𝐵𝐷=24.33cm, 𝐴𝐶=36.63cm
  • B𝐵𝐷=11.4cm, 𝐴𝐶=25.44cm
  • C𝐵𝐷=1.95cm, 𝐴𝐶=5.11cm
  • D𝐵𝐷=11.4cm, 𝐴𝐶=19cm

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