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
