Difference between revisions of "1999 AMC 8 Problems/Problem 5"
(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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| − | + | ==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. | ||
Revision as of 14:49, 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.
