Question

stephon has a square brick patio. he wants to reduce the width by 2 feet and increase the length by 2 feet. let x represent the length of one side of the square patio. write expressions for the length and width of the new patio. then find the area of the new patio if the original patio measures 10 feet by 10 feet.

Explanation:

Step1: Find the new - length and width expressions

The original side - length of the square patio is $x$. The width is reduced by 2 feet, so the new width $w=x - 2$. The length is increased by 2 feet, so the new length $l=x + 2$.

Step2: Find the area formula of the new patio

The area of a rectangle is $A=l\times w$. Substituting the expressions for $l$ and $w$ we found in Step 1, we get $A=(x + 2)(x - 2)$. Using the difference - of - squares formula $(a + b)(a - b)=a^{2}-b^{2}$, here $a=x$ and $b = 2$, so $A=x^{2}-4$.

Step3: Calculate the area when $x = 10$

Substitute $x = 10$ into the area formula $A=x^{2}-4$. Then $A=10^{2}-4=100 - 4=96$ square feet.

Answer:

The expressions for the length and width of the new patio are $x + 2$ and $x - 2$ respectively, and the area of the new patio when the original patio is 10 feet by 10 feet is 96 square feet.