equality problem?

Question

use two equations in two variables to solve the folowing question
at an IMAX theater, the giant rectangular movie screen has a width 13 feet less than its length. if its perimeter is 270 feet, find the area of the screen.

Answer 1

I see two unknowns, namely the width and the length.

Let's let:
W = width in feet
L = length in feet

The perimeter (distance around the screen) is the sum of the top and bottom sides (2L) plus the left and right sides (2W). This equals 270 feet.

For your first equation, you have:
2L + 2W = 270

You also know that the width is 13 feet less than the length. So your second equation is:
W = L - 13

Substitute W into the equation and solve:
2L + 2(L-13) = 270

Distribute the 2 through:
2L + 2L - 26 = 270

Combine the L terms:
4L - 26 = 270

Add 26 to both sides:
4L = 270 + 26

Simplify:
4L = 296

Divide both sides by 4:
L = 74

The length is 74 ft.

Now use this value of L to solve for W:
W = L - 13
W = 74 - 13
W = 61

The width is 61 ft.

So the screen is 74 ft. by 61 ft.

To find the area, you multiply length times width.

A = L * W
A = 74 * 61
A = 4,514

So the area of the screen is 4,514 sq. ft.

Answer 2

Let the breadth be x, the length is x + 13 ft

x + x+ 13 + x + x+13 = 270
4x+26=270
4x=270-26
4x= 244
x=244/4
x=61

lenght = 61+13 = 74

Area = l x b = 61 x 74

=4514 sq feet

Answer 3

w+13=length ==> 74 feet
w=width ==> 61 feet
(2w)+[2(w+13)]=270
2w+2w+26=270
4w+26-26=270-26
4w/4=244/4
w=61
61*74=4514
Answer==>4514 feet^2