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## Do you length of a rectangle is five times the width. If the length and width are both increased by 2, the new area would be 85. What is the

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Answer:The original of the given rectangle = 45 sq units.Step-by-step explanation:Here, let us assume the actual width of the rectangle =

aSo, the actual length of the rectangle = 5 x ( width) = 5 (a) =

5 aNow, the new width w’ = ( a + 2)

and the new length l’ = ( 5 a + 2)

AREA OF THE RECTANGLE = LENGTH x WIDTHSo, the area of the new rectangle = (a + 2)(5 a +2)

Also, new area = 85 ⇒

(a + 2)(5 a +2) = 85⇒ ( 5a +27) =0 or (a-3) = 0

⇒ a = -27/5 or a = 3

But,

a = Width of a rectangle , so a CANNOT be Negative⇒ a ≠ -27/5 and

a = 3So, the actual width of the rectangle = a = 3

The length of the rectangle = 5 a = 5 (3) = 15

The original area = Original L x Original W = 3 x 15 = 45 sq units.