The perimeter of a rectangular shop in the mall is 84 meters. The area is 416 square meters. What are the dimensions of the shop?

Answer 1

Hello!

First, identify the formulas that are used (perimeter and area).

The formula for perimeter is: P = 2L + 2W

The formula for area is: A = LW

Focus on perimeter first, isolating either the W or the L. For instance:

P = 2L + 2W

84 = 2L + 2W

(divide each term by 2)

42 = L + W

Solve for either L or W. I will show you solving for L.

42 - W = L

Substitute this new value for L in the area formula.

A = LW

416 = (42 - W)W

(distribute the W on the right side to each of the terms in the parenthesis)

416 = 42W - W^2

(subtract 416 to both sides)

42 W - W^2 - 416

Make sure to rearrange your algebraic expression so that the exponents are in descending order.

-W^2 + 42W - 416 OR

W^2 - 42W + 416

Use the FOIL method to solve.

FOIL = first, outer, inner, last

(W - 16) (W - 26)

Set each expression equal to 0 and solve.

W - 16 = 0

W = 16

W - 26 = 0

W = 26

Since width is generally smaller than length, you can assume that the width is 16 meters, and the length is 26 meters.

You can check your findings to make sure that they plug back into the original formulas.

P = 2L + 2W

84 = 2(26) + 2(16)

84 = 52 + 32

84 = 84

A = LW

416 = 26(16)

416 = 416

Answer 2

Perimeter of a rectangle

2l+2w

Area of a rectangle

lw (length x width)

Therefore

2l+2w=84 m

lw= 416 sq m

2l=84-2w

l= 42-w ( divided both sides by 2)

l=416/w ( if lw is 416 sq to find l divide product by width)

Length=Length...therefore

42-w= 416/w

Now multiple

42-w/1 × 416/w

w²-42w+ 416=0

(w-26) (w-16)

You can use quadratic formula if you know it..

l=26

2(26)+2(w)=84

52+2w=84

2w=84-52

2w=32 ( Divide both sides by 2)

w=16

To check

lw=26×16=416

There for

l=26 , w= 16

Answer 3

length plus width = 42

length times width = 416

16 x 26