Question

The diagram shows two joined rectangles. The total area of the compound shape ABCDEF is 36 cm^2. By considering the areas of the two rectangles, show that

2x^2 - 5x - 18 = 0 and hence find the value of length AB.

Answer 1

The value of AB is 9/2 or 4.5

Answer 2

4.5 cm

Explanation:

The total area is the sum of areas of two rectangles:

• x(x-4)+3x(x-2)=36
• x²-4x+3x²-6x-36=0
• 4x²-10x-36=0
• 2x²-5x-18=0
• 2x²-9x+4x-18=0
• x(2x-9)+2(2x-9)=0
• (x+2)(2x-9)=0
• x+2=0 ⇒ x= -2 discarded as negative
• 2x-9=0
• 2x=9
• x=4.5
• AB=4.5 cm