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A rectangular lot is 80 yards wide and 125 yards long.

Give the length and width of another rectangular lot that has the same perimeter but a smaller area.

User Wu Wei
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1 Answer

2 votes

Answer:

70 yards wide and 135 yards long

Explanation:

The perimeter of a rectangle will be the same if the sum of length and width is the same. The area will be smaller if the difference between lenth and width is greater.

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The sum of length and width will be the same if the length is increased by the same amount that the width is decreased. Changing each by 10 yards is one possibility.

A lot 70 yards wide and 135 yards long will have the same perimeter and a smaller area.

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Check

Given perimeter: 2(80 +125) = 410 yds.

Modified perimeter: 2(70 +135) = 410 yds. (same)

Given area = 80(125) = 10000 yd².

Modified area: 70(135) = 9450 yd². (smaller)

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Additional comment

The area is greatest when the difference between the length and width is zero. That is, the rectangle will be a square.

User Kwisatz
by
4.3k points