Math Prob 12?

Question

Find the length of the legs of a right triangle having perimeter 56m if the hypotenuse is 25m.

Answer 1

by pythagorean theorem, a2 + b2 = c2

c = 25
other sides are a and (31-a)

substitute into the formula to get
a^2 + (31-a)^2 = 25^2

you figure out the rest, I don't have a calculator right now

Answer 2

Let

a, b = legs of the triangle
c = hypotenuse of the triangle

Given

c = 25 m
a + b + c = 56 m

Find a and b.

a + b + 25 = 56
a + b = 31
a = 31 - b

a² + b² = c²
a² + (31 - a)² = 25²
a² + 961 - 62a + a² = 625
2a² - 62a + 336 = 0
a² - 31a + 168 = 0
(a - 7)(a - 24) = 0
a = 7 or 24

If a is one of the solutions, b is the other.

So the legs of the right triangle are 7 m and 24 m.

Answer 3

13m each.