Question

A right triangle has one leg that is 5 cm longer than the other leg and the hypotenuse is 25 cm long. How do you find the length of each leg?

Answer 1

$\huge\bold{ANSWER~:}$

• Let, 1 side as x than 2nd is 5cm longer than first , than 2nd = (x+5)

• We know that in right triangle sum of squares of two sides is equal to square of hypotenus.

${(x)}^{2} + {(x + 5)}^{2} = {(25)}^{2} \\ \\ {x}^{2} + {x}^{2} + 10x + 25 = 625 \\ \\ 2 {x}^{2} + 10x = 625 - 25 \\ \\ 2 {x}^{2} + 10 x = 600 \\ \\ {2x}^{2} + x = \frac{600}{10} \\ \\ {2x}^{2} + x = 60$