Question

The perimeter of an isosceles triangle is 32 inches. If the base is longer than half of the two other equal sides by 2 inches, find the length of all sides of this triangle.

Write as a equation.​

Answer 1

Explanation:

Let equal sides of an isosceles triangle = a inches

Base =
`(1)/(2)a+2` inches

Perimeter = 32 inches

a + a +
`(1)/(2)a+2` = 32

`2a + (1)/(2)a+2 = 32\\\\(2a*2)/(1*2)+(1)/(2)a+2=32\\\\(4a)/(2)+(1)/(2)a+2=32\\\\(5)/(2)a+2 = 32\\\\`

Subtract 2 from both sides

`(5)/(2)a=32-2\\\\(5)/(2)a=30\\\\a=30*(2)/(5)\\\\a=6*2`

a = 12 inches

base =
`(1)/(2)*12+2`

= 6 + 2

Base = 8 inches