Question

The perimeters of the triangles shown are equal. Find the side lengths of each triangle.

AB =
PQ=
QR =
BC=
AC =
PR =

Answer 1

3x +9 + 3x + 3x +8 = 3x + 3x + 4x + 6

9x + 17 = 10x + 6

x = 11

AB 42

BC 41

AC 33

PQ 33

QR 33

PR 50

Answer 2

x = 11

Explanation:

if the perimeters are equal then:

the perimeter of the first triangle : 3x + 9 + 3x + 3x + 8 = 9x + 17

the perimeter of the second triangle : 3x + 3x + 4x + 6 = 10x + 6 and

9x + 17 = 10x + 6 export like terms to the same side of the equation

17 - 6 = 10x - 9x

11 = x

we can find the lengths by replacing x with 11 in given expressions.