Math Question?

Question

The length of a rectangle is 4 ft longer than its width. If the perimeter of the rectangle is 36ft, find its area.

Answer 1

Okay. This can be a little tricky if you dont see how to set it up.

we don't yet know the length, so lets call that x. Since we all know there are 4 sides to a rectangle lets set up the equation like this.

36 = Perimiter. Since the length is 4 ft longer lets write the expression to show that.

36= 2(4+x)+2x

x = the width, and since theres 2 lengths and 2 widths, multiply them by two. now multiply out.

36= 2(4+x)+2x => 36=8+2x+2x => 36=8+4x

now its simple algebra

36-8=4x
28=4x
x=7

since x=width, width =7 ft
since x+4=length length = 11 ft

now find the area. This is the easy part.

Area= length x width

A= 11x7

A=77 ft^2

Answer 2

Math Question?

The length of a rectangle is 4 ft longer than its width. If the perimeter of the rectangle is 36ft, find its area.

width = (36 - 4 -4 ) divided by 4 = 7
length = 7 + 4 = 11

Area = 7 * 11 = 77ft square

Answer 3

Let x be the width of the reactangle

length = x+4
( given length 4 ft longer than width)

Perimeter = 2*(length+width)
(given perimeter = 36 ft)

2(x+4+x) = 36

4x+8 = 36

4x = 36-8
x = 7

width= 7ft, length = 11ft

Area = 7* 11

= 77 sq.ft.

Answer 4

Area = Length * Width --- (for a rectangle)
A = L * W
L = W + 4

Perimeter = 2(Length * Width) --- (for a rectangle)
P = 2(L + W)
2((W + 4) + W) = 36 --- Combine like terms...
2(2W + 4) = 36 --- Multiply 2 by the terms in the parenteses...
4W + 8 = 36 --- Subtract 8 from both sides...
4W = 28 --- Divide both sides by 4...
W = 7

Since we know that L = W + 4, and we know that W = 7:
L = 7 + 4
L = 11

A = L * W
A = 7 * 11
A = 77 feet²

Answer 5

Let the length of the rectangle be x and the width be y.

We now have two equations.

1. x+4 = y
2. 2x + 2y = 36 (perimeter)

x = y-4

Let us substitute the value of x into equation 2.

2(y - 4) + 2y = 36
2y -8 +2y = 36
4y = 44
y = 11

Then x must be 7, since x is y - 4.

Area of rectangle is length * width

= 7 * 11 = 77 sq. ft

Answer 6

If P = 2W + 2L

And you apply this problem P = 2W + 2(W+4)

Plug in the numbers 36 = 2W + 2W + 8

Simplify the problem 36 = 4W + 8

Get the variable by itself 36 - 8 = 4W - 8

..which equals 28 = 4W

Divide by 4 to get the variable by itself

...which equals 7. So now plug 7 into the problem

W=7
L=(7+4)=11

Area=7x11=77u^2

Answer 7

Perimeter = 2*Width + 2*Length
P = 2W + 2L

L = W + 4

P = 2W + 2(W + 4) = 36
2W + 2W + 8 = 36
4W = 28
W = 7

L = 7 + 4 = 11

A = LW = 11*7 = 77

Answer 8

just set up and equation.
2 times 4 plus 2w, plus w = 36

Answer 9

l=w+4
2(w+4)+2w=36
4w+8=36
4w=28
w=7'
l=11'
area=77 sft

Answer 10

w=x
l=x+4

2x+2(x+4)=36
2x+2x+8
4x=28
x=7
width is 7 and length is 11

A=wl
A=77ft^2