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 = -2
Since x i.e. length of a side can not be negative. So, x = 4.5 cm. (Answer)
