Triangles P and Q are right-angled - OCR - GCSE Maths - Question 21 - 2017 - Paper 1

To find the lengths of the two shorter sides in triangle P, we can apply the Pythagorean theorem.

Given triangle P:

• The hypotenuse is 13 cm
• One side (height) is 12 cm

Let the length of the other side be denoted as $a$. According to the Pythagorean theorem: $a^2 + 12^2 = 13^2$ Simplifying this gives: $a^2 + 144 = 169$ Subtracting 144 from both sides: $a^2 = 25$ Taking the square root: $a = 5 ext{ cm}$

Thus, the two shorter sides of triangle P are 12 cm and 5 cm.

In triangle Q, the two shorter sides are given as 12 cm and 5 cm. Therefore, both triangles have the same lengths for their shorter sides.