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1997 PMWC Problems/Problem I11: Difference between revisions

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330 cm.
==Problem==
A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is <math>6750 cm^2</math>.
[[Image:ABCD.gif]]
 
==Solution==
 
Let l and w be the length, and width, respectively, of one of the little rectangles.
 
<math>3w=2l</math>
 
<math>l=\dfrac{3}{2}w</math>
 
<math>6750=\dfrac{15}{2}w^2</math>
 
<math>w=30</math>
 
The perimeter of the big rectangle is
 
<math>2(w+l)+3w=330</math>

Revision as of 17:38, 8 October 2007

Problem

A rectangle ABCD is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of ABCD if its area is $6750 cm^2$.

Solution

Let l and w be the length, and width, respectively, of one of the little rectangles.

$3w=2l$

$l=\dfrac{3}{2}w$

$6750=\dfrac{15}{2}w^2$

$w=30$

The perimeter of the big rectangle is

$2(w+l)+3w=330$

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