1997 AMC 12 Problem 5

Attempt Problem 5 of the 1997 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1997 AMC 12 solutions, or check the answer key.

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A rectangle with perimeter

176

is divided into five congruent rectangles as shown in the diagram. What is the perimeter of one of the five congruent rectangles?

35.2

76

80

84

86

Let the short and long sides of a small rectangle be

x

and

y

The total width is both

3x

across the top and

2y

across the bottom

Let a small rectangle have sides

x

and

y.

The common width gives

3x=2y,

while the large rectangle has dimensions

3x

x+y.

Its perimeter is

2(4x+y)=176.

Since

y=\frac{3x}{2},

this is

11x=176,

x=16

and

y=24.

One small perimeter is

2(16+24)=80,

making C correct.

Problem 5 in other years