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 use the Pythagorean theorem. Given:

• Triangle P has sides of length 12 cm and 13 cm, so we need to find the length of the third side (hypotenuse).
• Let the hypotenuse be labeled as c.

Using the Pythagorean theorem:

$c^2 = a^2 + b^2$

Substituting the values:

$c^2 = 12^2 + 12^2$ $c^2 = 144 + 144 = 288$ $c = ext{sqrt}(288) = 12\sqrt{2} \text{ cm}$

For triangle Q, one side is 12 cm, and the other shorter side is 5 cm. Checking the lengths:

• The shorter sides of triangle Q are 12 cm and 5 cm.
• We need to compare these with triangle P.

Through calculations, we confirm that the two shorter sides in triangle P (12 cm and 12 cm) correspond to the shorter sides in triangle Q (12 cm and 5 cm). Thus, the shorter sides of triangle P are equivalent in length to those of triangle Q.