Question

The dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other. The area of the resulting rectangle is 126 in². What was the orriginal side length of the square?

Answer 1

Answer

Find out the original side length of the square .

To prove

Let us assume that the original length of the square be x.

Formula

$Area\ of\ rectangle = Length\times Breadth$

As given

The dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other.

Length becomes  = x + 8

Breadth becomes = x -3

The area of the resulting rectangle is 126 in²

Put in the formula

(x + 8) × (x - 3) = 126

x² -3x + 8x -24 = 126

x ²+ 5x = 126 +24

x² + 5x - 150 = 0

x² + 15x - 10x - 150 = 0

x (x + 15) -10 (x +15) =0

(x + 15)(x -10) =0

Thus

x = -15 , 10

As x = -15 (Neglected this value because the side of the square cannot be negative.)

Therefore x = 10 inches be the original side of the square.