The width of a rectangle is 6 in. less than its length. The perimeter is 68 in.

What is the width of the rectangle?

in.

Question

The width of a rectangle is 6 in. less than its length. The perimeter is 68 in.

 

What is the width of the rectangle?

 

in.

gabbyalicorn · Answer

Hi pooja.

pooja195 · Answer

Uh i think the answer is in the question....if im right

anonymous · Answer

divide it in two first

jhannybean · Answer

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jhannybean · Answer

Omg I forgot the shapes have the "fill" option.... anyway.

anonymous · Answer

yeah

gabbyalicorn · Answer

When you say divide two first, do you mean 68 ÷ 2 and 6÷ 2

anonymous · Answer

no 68 by 2

anonymous · Answer

then subtract 6 from that

gabbyalicorn · Answer

okay, that is 34...

jhannybean · Answer

the length of the rectangle is given, but they say the `width` `is (equal to)` the `length - 6 in`You can rewrite this as $\sf w = L-6$

jhannybean · Answer

So the Perimeter of a rectangle is represented as: $$\sf P = 2L +2W$$

jhannybean · Answer

Since we're given the perimeter, and that is = 68 in. we can substitute that in to our formula. $$\sf 68 = 2L +2W$$

jhannybean · Answer

But we also know something else, $\sf W=L-6$

gabbyalicorn · Answer

68 - 6?

jhannybean · Answer

So we can substitute this in to the formula for the perimeter. $$\sf 68 = 2L+2(L-6)$$

jhannybean · Answer

Are you following, @gabbyalicorn ?

gabbyalicorn · Answer

Um, somewhat... I don't really get it but i'm following the steps if that's what you mean. :)

jhannybean · Answer

Which part are you confused with? Let's clarify that before moving on.

gabbyalicorn · Answer

is L the variable we are trying to find

gabbyalicorn · Answer

the number for...

jhannybean · Answer

We are trying to find W (width). The problem indiscreetly gives us the equation for the width by saying that the width IS 6 LESS THAN the length. We can write an equation for that. $\sf w = L-6$

gabbyalicorn · Answer

but what is L

jhannybean · Answer

But we can't automatically find the width, $\sf w$ can we? We need to find the length, $\sf L$ first.

jhannybean · Answer

That is where we use the equation for the perimeter of the rectangle. $\sf P = 2L +2w$

jhannybean · Answer

Do you see how this works?

gabbyalicorn · Answer

I think I'm getting it...

jhannybean · Answer

Okay, so we have $$\sf 68 = 2L+2(L-6)$$ We need to first distribute (meaning multiply) 2 to each term inside the parenthesis. $$2 \cdot L =~?$$$$2\cdot (-6) =~?$$

gabbyalicorn · Answer

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