a rectangular shop in the mall has an area of 242 meters. It’s perimeter is 66 meters. What are the dimensions of the shop?

Answer 1

Hello, please take a look below!

Area = Length x Width

Perimeter = 2(Length) + 2(Width)

Let's represent length with L and width with W:

A = L x W

P = 2L + 2W

Substitute in the given values for A and P

242 = L x W

66 = 2L + 2W <--------- Notice how all terms are divisible by 2. Lets divide them all by 2 to get 33= L + W

So our system is:

242 = L x W

33 = L + W

We need to use the substitution method to solve this system of equations. Let's solve the area problem for L.

Divide each side of 242 = L x W by W ------------------> 242/W = L.

Substitute this into the perimeter equation.

33 = 242/W + W

Multiply all terms by W to get ride of the fraction 242/W

33 (W) = (242/W)(W) + W(W)

33W = 242 + W²

Subtract 33W over to the right side to set up factoring.

0 = W² - 33W + 242 <------------ now we can factor. What two numbers multiply to get 242 and add to

get -33? (-22 and -11)

0 = (W - 11) (W - 22)

Set each factor equal to 0 and solve.

W -11 = 0 -----> W = 11

W -22 = 0 -----> W = 22

Which factor is correct for the width? Since width is typically the shorter side, we will select W = 11.

Go back to your original system and substitute W = 11 into the Area equation to find length.

242 = L x 11

242 = 11L <-------- Divide both sides by 11.

22 = L.

CHECK: 22 X 11 = 242; 2(22) + 2(11) = 66.

Dimensions: 22 by 11.