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

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

...............(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)

Factorising ,

So we have two values of b

b=14 and b=48

If b=14, a=48

If b=48, a=14

The shorter leg will  be 14 inches.

table 1

step-by-step explanation:

1-16

2-32

4-64

8-128

all multiples of 16

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.