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1999 AMC 8 Problems/Problem 5: Difference between revisions

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Created page with "The perimeter of the rectangle is <math>50(2) + 10(2) = 100 + 20 = 120</math> feet. This fence is used for a square, which has four sides, so each side is <math>30</math> feet lo..."
 
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The perimeter of the rectangle is <math>50(2) + 10(2) = 100 + 20 = 120</math> feet. This fence is used for a square, which has four sides, so each side is <math>30</math> feet long.
==problem==


Now to compare areas. The area of the rectangle is <math>(50)(10)</math>, or <math>500</math> square feet. The square's area is <math>30^2</math> square feet, or <math>900</math> square feet. Subtracting the rectangular area from the square area, we have an increase of <math>400</math> square feet.
A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To
make the garden larger, while using the same fence, its shape is changed to a
square. By how many square feet does this enlarge the garden?
(A) 100 (B) 200 (C) 300 (D) 400 (E) 500
 
==solution==
 
(D) 400 square feet: The area of the garden was 500
square feet(50£10) and its perimeter was 120 feet,
2 £ (50 + 10). The square garden is also enclosed
by 120 feet of fence so its sides are each 30 feet
long. The square garden's area is 900 square feet
(30 £ 30). and this has increased the garden area
by 400 square feet.

Revision as of 13:49, 4 November 2012

problem

A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden? (A) 100 (B) 200 (C) 300 (D) 400 (E) 500

solution

(D) 400 square feet: The area of the garden was 500 square feet(50£10) and its perimeter was 120 feet, 2 £ (50 + 10). The square garden is also enclosed by 120 feet of fence so its sides are each 30 feet long. The square garden's area is 900 square feet (30 £ 30). and this has increased the garden area by 400 square feet.

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