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 is 126 in^2. What was the original side length of the square.

Answer 1

`Original\ length\ of\ square=10\ inches`

Explanation:

Let the length of square
`=x\ inches`

`8` inches is added one side of square

Then length of one side
`=x+8\ inches`

`3\ inches` is subtracted other side of square

Then length of other side
`=x-3`

`area\ of square =126\ inches^2\\\\Side* side =126\ inches^2\\\\(x+8)*(x-3)=126\ inches^2\\\\x(x-3)+8(x-3)=126\ inches^2\\\\x^2-3x+8x-24=126\ inches^2\\\\x^2+5x-24=126\ inches^2\\\\x^2+5x-150=0\\\\x^2+15x-10x-150=0\\\\x(x+15)-10(x+15)=0\\\\(x+15)(x-10)=0\\\\x+15=0\\x=-15\ \ \ \ negative\ length\ does\ not\ consider\\\\x-10=0\\x=10`

`Original\ length\ of\ square\ =10\ inches`