Question

One leg of a right triangle is 7 feet longer than the other leg. The hypotenuse is 13 feet. Find the lengths of the two legs

Answer 1

Answer:

The other two legs are 12 feet and 5 feet. Please mark me as brainliest.

Step-by-step explanation:

Let leg1 be a, and Leg2 be b, and hypotenuse be c

$c^2 = a^2 + b^2\\13^2 = a^2 + (a - 7)^2\\169 = a^2 + a^2 - 14a + 49\\2a^2 -14a + 49 - 169 = 0\\2a^2 - 14a - 120 = 0\\2a^2 - 24a + 10a - 120 = 0\\2a(a - 12) + 10(a - 12) = 0\\(a - 12)(2a + 10) = 0$

a - 12 = 0 or 2a + 10 = 0

a = 12 or a = -10/2 = -5

a can't be negative, so, a = 12, a - 7 = 5