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 original area?

The original of the given rectangle = 45 sq units.

Step-by-step explanation:

Here, let us assume the actual width of the rectangle = a

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

Now, the new width w'  = ( a + 2)

and the new length l' =  ( 5 a + 2)

AREA OF THE RECTANGLE = LENGTH x WIDTH

So, 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 =  3

So, 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.

step-by-step explanation:

107 units