Question

Stacey has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches off of the width. The area of the smaller square is 1/4the area of the original square. What was the side length of the original square?

Answer 1

Answer:

The side length of the original square was 6 inches

Step-by-step explanation:

we know that

The area of a square is

$A=b^2$

where

b is the length side of the square

Let

x ---> the length of the original square

The area of the original square is

$A=x^{2}\ in^2$

The length of the smaller square is

$b=(x-3)\ in$

The area of the smaller square is

$A=(x-3)^2\ in^2$

The area of the smaller square is 1/4 the area of the original square

so

$(x-3)^2=\frac{1}{4} x^{2}$

solve for x

$x^2-6x+9=\frac{1}{4} x^{2}$

Multiply by 4 both sides

$4x^2-24x+36=x^{2}$

$4x^2-x^2-24x+36=0\\3x^2-24x+36=0$

Solve the quadratic equation by graphing

using a graphing tool

x=2, x=6

see the attached figure

The solution is x=6 in

Remember that the solution must be greater than 3 inches (because Stacey cuts  3 inches off of the length of the square and 3 inches off of the width)

therefore

The side length of the original square was 6 inches