In the diagram all measurements are in centimetres.
The perimeter of the quadrilateral is twice the perimeter of the triangle.
Work out the perimeter of the quadrilateral.

Perimeter of the quadrilateral = 48 cm

Solution:

The dimensions of the quadrilateral are 2x, 2x – 1, x – 3 and 3x.

The dimensions of the triangle are x + 3, 5 and x + 3.

Perimeter of the polygon = Sum of the sides of the polygon

The perimeter of the quadrilateral  = 2 × Perimeter of the triangle

2x + 2x – 1 + x – 3 + 3x = 2 × (x + 3 + 5 + x + 3)

8x – 4 = 2 × (2x + 11)

8x – 4 = 4x + 22

Add 4 on both sides of the equation.

8x = 4x + 26

Subtract 4x on both sides of the equation.

4x = 26

Divide by 4 on both sides of the equation.

x = 6.5

Perimeter of the quadrilateral  = 2 × (x + 3 + 5 + x + 3)

Perimeter of the quadrilateral = 2 × (6.5 + 3 + 5 + 6.5 + 3)

                                                  = 2 × (9.5 + 5 + 9.5)

                                                  = 2 × 24

                                                  = 48

Perimeter of the quadrilateral = 48 cm

step-by-step explanation:

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