Question

one side of a rectangle is 4 feet shorter than four times the other side. find the sides of the are if the rectangle is 24 square feet

Answer 1

The first side of the rectangle = 3 ft

The other side = 8 ft

Explanation:

Let the one side of the rectangle = k feet

So, the other side of the rectangle = 4 ( First side) -4 = (4 k -4 ) ft

Now, the area of the given same rectangle = 24 sq ft

Area of the RECTANGLE = LENGTH x WIDTH

⇒ Area = k x ( 4k - 4)

or, k ( 4k - 4) = 24

`\implies 4k^2 - 4k  = 24\\\implies k^2 - k = 6\\\implies k^2 - k - 6  = 0\\\implies k^2 - 3k + 2k - 6 = 0`

or, k(k-3) +2(k-3) = 0

or, (k-3)(k+2) = 0

or, k = 3, or k = -2

As k = Length of the rectangle, so CAN NOT BE NEGATIVE.

⇒ k ≠ -2 , ⇒ k = 3 ft

So, the first side of the rectangle = k = 3 ft

The other side = 4 k - 4 = 4 (3) - 4 = 12 - 4 = 8 ft