Answer:
The area of the original rectangle = 189 sq ft.
Step-by-step explanation:
Let, the width of the rectangle = m feet
So, the length of the rectangle = (2 m + 3) ft
Now, new width w' = (m + 4)
Perimeter of new rectangle (P') = 68 ft
Perimeter of a rectangle = 2 (LENGTH + WIDTH)
⇒68 ft = 2( L + W')
or, 68 ft = 2 [( 2m + 3) + (m + 4)]
or, 2 (3m + 7) = 68
or, 3m + 7 = 68/2 = 34
⇒ 3m = 34 - 7 = 27
⇒ m = 27/3 = 9
or, m = 9 ft
Hence, the original width of the rectangle = 9 ft
Original Length of the rectangle = 2m + 3 = 2(9) + 3 = 21 ft
Now, Area of the Rectangle = LENGTH X WIDTH
= 21 ft x 9 ft = 189 sq ft
Hence,the area of the original rectangle = 189 sq ft.
