Mr. Smith is installing a gravel path along the diagonal of a rectangular garden. The garden measures 40 feet by 30 feet. If the path is 3 f

Question

Mr. Smith is installing a gravel path along the diagonal of a rectangular garden. The garden measures 40 feet by 30 feet. If the path is 3 feet wide, and the gravel costs $2.50 a square foot, how much will it cost to install the gravel path? (I mean just the cost of the gravel)

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Serenity 4 months 2021-09-11T11:53:58+00:00 1 Answer 0 views 0

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    2021-09-11T11:55:36+00:00

    Answer: it will cost $375 to install the gravel path

    Step-by-step explanation:

    The diagonal of the rectangular garden divides it into two equal right angle triangles. The diagonal represents the hypotenuse of each right angle triangle. The length and width of the rectangle represents the adjacent and opposite sides of the right angle triangle. To determine the length of the diagonal, d, we would apply Pythagoras theorem which is expressed as

    Hypotenuse² = opposite side² + adjacent side²

    Therefore

    d² = 40² + 30²

    d² = 1600 + 900 = 2500

    d = √2500

    d = 50 feet

    If the path is 3 feet wide, then the area of the path is

    Area = 50 × 3 = 150 ft²

    If gravel costs $2.50 a square foot, then the cost to install the gravel path is

    2.5 × 150 = $375

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