Question

Which side lengths form a right triangle?

Answer 1

Answer:

$(a)\ 5, \sqrt 6, \sqrt{31$

$(c)\ 9, 12, 15$

Step-by-step explanation:

Required

Side lengths that form a right triangle

Applying Pythagoras theorem

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

Where a is the longest side.

So, we have:

$(a)\ 5, \sqrt 6, \sqrt{31$

$(\sqrt{31})^2 = 5^2 + (\sqrt 6)^2$

$31 = 25 + 6$

$31 = 31$

This forms a right triangle

$(b)\ \sqrt 5, \sqrt 5, 50$

$50^2 = (\sqrt 5)^2 + (\sqrt 5)^2$

$2500 = 5 + 5$

$2500 \ne 10$

This does not form a right triangle

$(c)\ 9, 12, 15$

$15^2 = 12^2 + 9^2$

$225 = 144 + 81$

$225 = 225$

This forms a right triangle