A square and a rectangle have the same perimeter. The square has a length and width of 4 and the rectangle has a length of 5. What is the area of the rectangle? A. 3 B. 6 C. 15 D. 30 Solution:
Since the perimeter of the square is 4 X 4 = 16, the perimeter of the rectangle is also 16. The length of the rectangle is given as 5. Let w be the width of the rectangle. So, the perimeter (sum of all the sides) of the rectangle is 2 X 5 + 2 X w. This expression is equal to 16 and let's us then solve for w as below: 2 X 5 + 2 X w = 16 10 + 2w = 16 2w = 6 w = 3 We found the width to be 3, and the length is 5, so the area is 3 X 5 = 15. Hence, the answer is C: 15.
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