Question

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

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

Answer 1

AB = 51

BC = 50

AC = 42

PQ = 42

QR = 42

PR = 59

Explanation:

Perimeter of ∆ ABC = Perimeter of ∆ PQR

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

9x + 17 = 10x + 3

17 - 3 = 10x - 9x

14 = x

.: x = 14

AB = 3x +9 = 3×14+9 = 42+9 = 51

BC = 3x +8 = 3×14+8 = 42+8 = 50

AC = 3x = 3×14 = 42

PQ = 3x = 3×14 = 42

QR = 3x = 3×14 = 42

PR = 4x +3 = 4×14+3 = 56+3 = 59