Question

7. Which dimensions result in the minimum perimeter for a rectangle with area 42.0 cm2?

a. l = 9.00 cm, w = 4.67 cm c. l = 1.00 cm, w = 42.00 cm
b. l = 5.00 cm, w = 8.40 cm d. l = 6.48 cm, w = 6.48 cm

8. The minimum perimeter occurs when the rectangle is a _____.

a. quadrilateral c. parallelogram
b. triangle d. square

Answer 1

9514 1404 393

Answer:

7. d. l = 6.48 cm, w = 6.48 cm

8. d. square

Explanation:

For a given area, the perimeter can always be shortened by reducing the length of the long side and increasing the length of the short side. When you get to the point where you can't do that, then you have the minimum perimeter. You will reach that point when the sides are the same length: the rectangle is a square.

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7. In light of the above, the best dimensions are √42 ≈ 6.48 cm for length and width.

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8. In light of the above, the shape is a square.

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The attached graph shows the length of one side (x) and the associated perimeter. The other side is 42/x, which will also be 6.48.