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.


A. lw = (x + 2)(x – 2); 96 square feet

B. lw = (x – 2)(x – 2); 64 square feet

C. lw = x(x – 2); 80 square feet

D. lw = (x + 2)(x + 2); 144 square feet

Answer 1

A

reducing one side by 2 is expressed as (x - 2) ← length

increasing the other side by 2 is expressed as (x + 2 ) ← width

the area of new patio = (10 - 2 )(10 + 2) 8 × 12 = 96 ft²

Answer 2

Answer: A. lw = (x + 2)(x – 2); 96 square feet

Step-by-step explanation:

Given: Stephon has a square brick patio. He wants to reduce the width by 2 feet and increase the length by 2 feet.

Let x be the side-length of the patio, then

The length of the patio after change = x+2

The width of the patio  after change = x-2

Then the area of the patio is given by :-

$A=lw\\\Rightarrow\ A=(x+2)(x-2)$

If the original patio measures 10 feet by 10 feet.

Then the area of the patio= $(10+2)(10-2)=(12)(8)=96$ square feet.

Hence, A is the right answer.