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.


Find 𝑥 in the right triangle shown.


Find 𝑥 in the right triangle shown.


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.


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


Find the perimeter of 𝐴𝐵𝐶𝐷.


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


Which of the relations below is correct?

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


Find the length of 𝐷𝐶 in the trapezoid 𝐴𝐵𝐶𝐷.


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.


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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