The perimeter of a rectangle is 68 ft. Find the dimensions of the rectangle if the ratio of the length to the width is 9 : 8. Which of the following would be the best equation to use to solve this problem?

Question

The perimeter of a rectangle is 68 ft. Find the dimensions of the rectangle if the ratio of the length to the width is 9 : 8.  Which of the following would be the best equation to use to solve this problem?

k_lynn · Answer

Here it is.

k_lynn · Answer

@iambatman

k_lynn · Answer

can you help me?

k_lynn · Answer

@e.mccormick would you be able to help me with this?

anonymous · Answer

What is the perimeter of a rectangle?

k_lynn · Answer

68ft.

anonymous · Answer

what is the equation look like

k_lynn · Answer

Well for this one at least.

anonymous · Answer

Do you know what a perimeter is

k_lynn · Answer

ya, the amount of all the sides of a shape.  Say all the sides of a square were 4in.  the perimeter would be 16in.

anonymous · Answer

Ok so make an equation for a rectangle,

k_lynn · Answer

I'm just not sure how to use an equation to solve it.

k_lynn · Answer

I'm thinking its D. But I'm not entirely sure.

anonymous · Answer

Hint: |dw:1418860775289:dw| what is the perimeter of this?

k_lynn · Answer

l*2+w*2

k_lynn · Answer

Well now, I'm kind of thinking its B.

anonymous · Answer

It's actually just 2l+2w = 68 haha

k_lynn · Answer

Ok, so A then?

anonymous · Answer

Bingo

k_lynn · Answer

Ok, thank you.

anonymous · Answer

Don't let the ratio confuse you ;)

k_lynn · Answer

I'll try not to.

e.mccormick · Answer

Actually, the ratio is not there to confuse you.  You are trying to find the actual dimensions, which the ratio lets you do.

e.mccormick · Answer

A only works if it is a square.  It is not a square, therefore A is wrong.
B is a fraction so would have nothing to do with a paremeter, so wrong.
C does not account for there being 2 of each side, so wrong.
D, on the other hand, does account for the ratio and four sides.

k_lynn · Answer

Oh, ok thanks.  That really clears some things up.

e.mccormick · Answer

9x+9x+8x+8x=68
18x+16x=68
18x+16x=68
34x=68
x=2

Therefore, the long side is 18 and the short side is 16.

I can confirm by going back to the base formula:

2l+2w=68
2(18)+2(16)=68
36+32=68
68=68

None of the others are actually able to do that.

anonymous · Answer

Well that is true you can do 9x+9x+8x+8x=68 =>34x=68 => x = 2 and use this to check the for parameter haha.

k_lynn · Answer

Thank you, that's really helpful.  I think I get this now.

e.mccormick · Answer

Yah, the ratio was there as information.  However, the fraction was there to confuse you because they used the word ratio and the two are somewhat interchangable.

e.mccormick · Answer

A looks a lot like the actual formula, 2l+2w=P, but note they used x only and not x and y, so it is really the perimeter of a square!  4x=P for a square.  C was similarly flawerd because it had the ratio but not the 2!