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A rectangular pyramid has a base that is three times as long as it is wide. The volume of the pyramid is V cubic feet and the height is 3 ft. What is the perimeter of the base?

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Final answer:

To find the perimeter of the base of the rectangular pyramid, first find the width using the volume and height, then calculate the perimeter as 8 times the width.

Step-by-step explanation:

The question asks for the perimeter of the base of a rectangular pyramid with a known volume V and a height of 3 ft. The base is described as three times as long as it is wide.

Using the formula for the volume of a pyramid, V = (1/3) × base area × height, we can find the area of the base (A). Let the width of the base be w and the length be 3w. Then, the area of the base is A = w × 3w = 3w².

Given that the height is 3 ft, we rearrange the volume formula to solve for the base area: base area = 3 × (V/3). Therefore, the base area is equal to the volume V (since the 3s cancel out).

Now, we can equate 3w² to V and solve for w. Once we find w, the perimeter of the base is the sum of all sides: P = 2w + 2 × (3w) = 8w.

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