# Word Problem: A parking lot measures 100 by 130 feet.

#### pochoa

##### New member
I can not figure out what formula I should be using for this! Heres the problem:

A parking lot measures 100 by 130 feet. A sidewalk of uniform width is to completely surround the lot. If the sidewalk covers 1659 sq ft. how wide can the sidewalk be?

Can anyone help me get started? Thanks!

#### stapel

##### Super Moderator
Staff member
pochoa said:
I can not figure out what formula I should be using for this!
There is no one "master formula" that will solve every word problem. You generally need to create the formula for each problem.

pochoa said:
A parking lot measures 100 by 130 feet. A sidewalk of uniform width is to completely surround the lot. If the sidewalk covers 1659 sq ft. how wide can the sidewalk be?
Have you made a drawing yet?

Eliz.

#### pochoa

##### New member
Yes I have. This is what I have so far:

(100+2x)(130+2x)=1659

4x^2+460-1659=0

Does this seem right so far? If so, where do I go from here? Factor? Quad . eq?

#### stapel

##### Super Moderator
Staff member
pochoa said:
This is what I have so far: (100+2x)(130+2x)=1659
Isn't the "1659" the area of the walk alone? That is, doesn't that measure exclude the inner 13000 ft<sup>2</sup> parking lot?

And since the parking lot is bigger than 1659, then 1659 cannot be the sum of the lot's and the walk's area, can it...?

Eliz.

#### Denis

##### Senior Member
pochoa said:
(100+2x)(130+2x)=1659
4x^2+460-1659=0
HOW in heck do you get 4x^2 + 460 as the result of (100+2x)(130+2x) :?:
That should be 4x^2 + 460x + 13000;
guess it don't matter too much: equation is not correct (as Stapel told you).

#### pochoa

##### New member
ok, i redid the problem . I got 3.5 ft for the answer. Am I still way off? thanks!

#### Denis

##### Senior Member
That's correct; 4x^2 + 460x - 1659 = 0 ; x = 3.5