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Geometry, area

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Geometry, area

by datonman » Fri Oct 30, 2015 12:32 pm
A certain figure shows a modern painting that consists of four differently colored rectangles, each of which has length 'l' and width 'w'. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles?

A.)15
B.)20
C.)25
D.)30
E.)40

Here is the picture of it from the book. I don't know how 'l' = 3w

I have an answer to this and it involves the explanation that 'l' = 3w and plugging it in the equation l(w+l). How does one get 'l' = 3w? P.S. it's number 73.
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by GMATGuruNY » Fri Oct 30, 2015 12:53 pm
datonman wrote:I don't know how 'l' = 3w
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The left side of the painting is represented by L.
The right side of the painting is represented by W+W+W.
Since the two sides are equal, we get:
L = W+W+W
L = 3W.
Thus, the height of the painting = 3W.

As the figure illustrates, base of the painting = W+L = W+3W = 4W.

Since the area of 4800 is equal to base x height, we get:
(4W)(3W) = 4800
12W² = 4800
W² = 400
W = 20.

The correct answer is B.
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by [email protected] » Sat Oct 31, 2015 1:21 pm
Hi datonman,

Since each of the 4 rectangles has the SAME length (L) and the SAME width (W), they are 4 IDENTICAL rectangles. Those 4 rectangles form a larger rectangle - you can see (visually) that the 3 'widths' = 1 'length.' From there, the rest of the math is just algebra.

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