Question

Q14

Answer 1

Answer:

42.6cm

Step-by-step explanation:

The sum total of all the sides of the shape is the perimeter of the shape. Hence;

Perimeter = x+3 + 4 + x+9 + 2x+5

Perimeter = 4x + 21

Given

Area of the figure = 75cm^2

Area = (x+3)(2x+5) + (2x+1)(6)

75 = 2x²+5x+6x+15+12x+6

75 =  2x²+23x+21

2x²+23x+21-75 = 0

2x²+23x-54 = 0

x = -23±√23²-4(2)(-75)/4

x = -23±√529+600/4

x = -12±√1129/4

x = -12+33.6/4

x = 21.6/4

x = 5.4

Recall that;

Perimeter = 4x+21

Perimeter = 4(5.4) + 21

Perimeter = 21.6+21

Perimeter = 42.6cm

Hence the perimeter is 42.6cm