The length of a rectangle is five times as long as it's width.

Question

The length of a rectangle is five times as long as it's width. If it has a perimeter of 120 cm, find it's area.

Answer 1

Perimeter = 2L + 2W

 

We know the perimeter is 120

 

therefore, 120 = 2L +2W

 

We also know that L = 5W

 

So we can substitute 5W in for L :  120 = 2(5W) + 2W = 10W +2W = 12W

 

120 = 12W  Divide both sides by 12

 

10 = W

If 10 = W then 5W = 50 = L

 

ANSWER:  Area is length times width    LW  =  50(10)  = 500 cm²

Answer 2

Perimeter = 120cm

Perimeter is the total length and width of all of the sides. Its a rectangle, so its four sides. I'd suggest drawing this out.

 

This is the equation for perimeter:

P=2L+2W

120=2L+2W

 

We dont know what the width is so it is 'W'.
They told us that the length is "5 times the width." Therefore, this would be 5 times W, or '5W'.

 

Lets plug in what we already know:

 

120=2(5W)+2(W)

120=10W+2W

120=12W

10=W

 

If the width is 10

L=5W

L=5(10)

L=50

 

Now we have that W=10 and L=50.

 

This makes sense because if the perimeter is 120, we would have:

10+10+50+50.

Or, 2(L)+2(W).

Or, 2(10)+2(50) = 120

 

Now, they want us to give them the area:

 

A=LxW.

The area = the length times the width.

 

Therefore: 

 

A= 10(50)

A= 500cm.