Question

the area of a square can be quadrupled by increasing the side length and width by 4 inches. what is the side length?

Answer 1

The number could be anything because whatever it is it can be quadrupled

Answer 2

Let the original side of the square be x inches.When sides are increased by 4 inches the sides are x+4 inches.

Area of square with side x inches= $x^{2}.$

Area of square with sides x+ inches=$(x+4)^{2}.$

According to question:The area of a square can be quadrupled by increasing the side length and width by 4 inches.\

Or $4x^{2}=(x+4)^{2}$

Expanding we have:

$4x^{2}=x^{2}+8x+16.$

Or,$3x^{2}-8x-16=0.$

Factoring,

(3x+4)(x-4)=0

3x+4=0   or  x=4

x=$-\frac{4}{3}.$ Or x=4.

Sides can not be negative so x=4.

The sides of the square will be 4 inches.