Difference between revisions of "1997 PMWC Problems/Problem I11"

Latest revision as of 11:44, 13 August 2014

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 $6750\text{ cm}^2$ .

$[asy] import cse5; import olympiad; size(4cm); pathpen=black; pair A=(0,0),B=(0,-2.5),C=(3,-2.5),D=(3,0); D(MP("A",A,W)--MP("B",B,W)--MP("C",C,E)--MP("D",D,E)--cycle); D((0,-1.5)--(3,-1.5)); D((1,0)--foot((1,0),(0,-1.5),(3,-1.5))); D((2,0)--foot((2,0),(0,-1.5),(3,-1.5))); D((1.5,-1.5)--(1.5,-2.5));[/asy]$

Solution

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

$3w=2l$

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

$6750= 5lw = \dfrac{15}{2}w^2$

$w=30$

$l=45$

The perimeter of the big rectangle is

$2(w+l)+6w=330$

1997 PMWC (Problems)
Preceded by Problem I10	Followed by Problem I12
I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10

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Difference between revisions of "1997 PMWC Problems/Problem I11"

Latest revision as of 11:44, 13 August 2014

Problem

Solution

See Also

@@ Line 1: / Line 1: @@
 ==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>.
+A rectangle <math>ABCD</math> is made up of five small congruent rectangles as shown in the given figure. Find the perimeter, in cm, of <math>ABCD</math> if its area is <math>6750\text{ cm}^2</math>.
-[[Image:ABCD.gif]]
+<asy>
+import cse5;
+import olympiad;
+size(4cm);
+pathpen=black;
+pair A=(0,0),B=(0,-2.5),C=(3,-2.5),D=(3,0);
+D(MP("A",A,W)--MP("B",B,W)--MP("C",C,E)--MP("D",D,E)--cycle);
+D((0,-1.5)--(3,-1.5));
+D((1,0)--foot((1,0),(0,-1.5),(3,-1.5)));
+D((2,0)--foot((2,0),(0,-1.5),(3,-1.5)));
+D((1.5,-1.5)--(1.5,-2.5));</asy>
 ==Solution==