see the attachment, I don't know how to get the answer
Accepted Solution
A:
Answer: [tex]2x^{2} -5x-18 = 0[/tex]x = 4.5 cm.Step-by-step explanation:There are two rectangles in the compound shape ABCDEF.The area of the small rectangle is x (x - 4) sq. cm.Again the area of the large rectangle is (x - 2) (2x + x) = 3x (x - 2) sq. cm.Therefore, the total are is x (x - 4) + 3x (x - 2) = 36 {Given}⇒ [tex]x^{2} -4x+3x^{2} -6x =36[/tex]⇒ [tex]4x^{2} -10x -36 =0[/tex]⇒ [tex]2x^{2} -5x-18 = 0[/tex] (Shown)Now, solving this equation we get [tex]2x^{2} -9x+4x-18 = 0[/tex]⇒ [tex](2x-9) (x+2) =0[/tex]⇒ x = 4.5 and x = -2Since x i.e. length of a side can not be negative. So, x = 4.5 cm. (Answer)