Respuesta :
Answer:
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
[tex]\implies 5a^2 + 10 a + 2a + 4 = 85\\\implies 5a^2 + 12a - 81 = 0\\\implies 5a^2 - 15 a + 27 a - 81 = 0\\\implies 5a(a -3) + 27(a -3) = 0\\\implies (5a +27)(a-3)= 0[/tex]
⇒ ( 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.
