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2nd degree equations, rectangles

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2nd degree equations, rectangles

by datonman » Tue Oct 20, 2015 12:01 pm
This question was kind of tricky. Reason being using how and when to attempt to use the formula(i'm assuming so correct me if i'm wrong in this regard as well.) L X W

A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

A.)3
B.)4
C.)6
D.)8
E.)9
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by GMATGuruNY » Tue Oct 20, 2015 1:15 pm
datonman wrote:A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

A.)3
B.)4
C.)6
D.)8
E.)9
Total area = (area of the photo) + (area of the border) = (10*8) + 144 = 224.

We can PLUG IN THE ANSWERS, which represent the width of the border.
When the correct answer choice is plugged in, the total area will be 224 square inches.

Answer choice B: 4
The following figure is implied:
Image
In this case, total area = bh = (4+10+4)(4+8+4) = (18)(16) = 288.
Since the total area must be LESS THAN 288, the width of the border must be LESS THAN 4.

The correct answer is A.

Answer choice A: 3
The following figure is implied:
Image
In this case, total area = bh = (3+10+3)(3+8+3) = (16)(14) = 224.
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by MartyMurray » Wed Oct 21, 2015 9:18 pm
datonman wrote:This question was kind of tricky. Reason being using how and when to attempt to use the formula(i'm assuming so correct me if i'm wrong in this regard as well.) L X W

A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

A.)3
B.)4
C.)6
D.)8
E.)9
There are many ways to handle this one. The way Mitch described is nice.

Alternatively you could just use L x W. If you see that way first, doing that might be the way to go.

My first idea was to do this one the following way.

L x W of the picture = 10 x 8 = 80

Area of the picture + border is 80 + 144 = 224

If x is the width of the border, (10 + 2x)(8 + 2x) = 224.

I could multiply the whole thing out and all that, but I'd rather not if I don't have to, and seeing as all the answer choices are integers, I bet I can easily figure out how to get the answer by finding integer factors of 224.

I know that 15 x 15 = 225. Maybe 16 x 14 = 224? Hmm. 16 x 15 = 240. So 16 x 14 = 224. Perfect.

So 10 + 2x = 16 and 8 + 2x = 14. So x = 3 and the correct answer is A.
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