Question

What length is the shorter leg of a right triangle that has hypotenuse 50 in long and its perimeter is 112 inches?

Answer 1

The perimeter of a triangle is given by:

Perimeter = sum of three sides

We are given perimeter = 112 in.

Hypotenuse = 50 in.

Let us say the other two sides are a and b.

So , we have

$a+b+50 =112$

$a+b =62$

$a =62-b$...............(2)

In a right angle triangle we can apply pythagorean theorem,

a² + b² = c²

here c is hypotenuse which is 50 in.

a²+b² = 50²

a²+b² = 2500............(2)

Plugging the value of a from equation (1) in (2)

$(62-b)^{2}+b^{2}=2500$

$3844-124b+(b)^{2}+b^{2}=2500$

$2(b)^{2}-124b+1344=0$

Factorising ,

$(b-14)(b-48)=0$

So we have two values of b

b=14 and b=48

If b=14, a=48

If b=48, a=14

Answer: The shorter leg will  be 14 inches.