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Answer :
Final answer:
To find the dimensions of the trailer's side with an area of 500 square feet and a length 5 times the height, we set up the equation 500 = 5h × h and solve for h. The height is 10 feet, and the length is 5 times the height, so it is 50 feet.
Explanation:
The student wants to determine the dimensions of the side of a trailer with an area of 500 square feet and where the length is 5 times the height. To find the dimensions, we set up the equation for the area of a rectangle, which is length times width (or in this case, height). Let h be the height of the trailer, and 5h be the length. The area A is then expressed by the equation: A = length × height, which is 500 = 5h × h.
Solving for h, we divide both sides of the equation by 5, giving h^2 = 100, and take the square root of both sides to find h = 10 feet. The length of the trailer is 5 times the height, so the length is 5 × 10 = 50 feet. Therefore, the dimensions of the side of the trailer are height: 10 feet and length: 50 feet.
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