Question

The base of an isosceles triangle is one half as long as each of the congruent sides. The perimeter is 55 in. How long is the base?

Answer 1

The base is 11 inches long

Explanation:

we know that

An isosceles triangle has two equal sides and two equal interior angles

Let

y -----> is the length of the base of the isosceles triangle

x ----> is the length of each of the congruent sides

The perimeter of the triangle is equal to

`P=y+x+x`

`P=y+2x`

we have

`P=55\ in`

so

`55=y+2x` ----> equation A

`y=(x)/(2)` ----> equation B

solve the system by substitution

substitute equation B in equation A

`55=(x)/(2)+2x`

solve for x

`55=(5)/(2)x`

`x=55(2)/5\\x=22\ in`

Find the value of y

`y=(x)/(2)` ---->
`y=(22)/(2)=11\ in`

therefore

The base is 11 inches long