Question

Side 1 of a triangle is three more than twice the length of side 2. Side 3 is five less than four times the length of side 2. the perimeter of the triangle is 89 inches. What is the length of each side of the triangle?

Answer 1

side 1 : 13 in , side 2 : 29 in , side 3 : 47 in

Explanation:

let side 2 be represented by x , then

side 2 : x

side 1 : 2x + 3

side 3 : 4x - 5

the perimeter is the sum of the 3 sides

given perimeter = 89 in , then sum the 3 sides and equate to 89

x + 2x + 3 + 4x - 5 = 89 ( collect like terms on left side )

7x - 2 = 89 ( add 2 to both sides )

7x = 91 ( divide both sides by 7 )

x = 13

Then

side 1 = 2x + 3 = 2(13) + 3 = 26 + 3 = 29

side 3 = 4x - 5 = 4(13) - 5 = 52 - 5 = 47

the lengths of the 3 sides are 13 in, 29 in and 47 in