A set of shelves fits an attic room with one sloping wall. the left edges of the shelves line up vertically, and the right edges line up along the sloping wall. the shortest shelf is 32 in. long, and the longest is 40 in. long. given that the three shelves are equally spaced vertically, what total length of shelving is needed?

Question

Mathematics

Dominick Warren

20 August, 22:35

A set of shelves fits an attic room with one sloping wall. the left edges of the shelves line up vertically, and the right edges line up along the sloping wall. the shortest shelf is 32 in. long, and the longest is 40 in. long. given that the three shelves are equally spaced vertically, what total length of shelving is needed?

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Nicholas Delacruz · Answer 1

108 inches of shelving is needed in total. This is because the shelves form a trapezoid. The short shelf + the longest shelf (32 + 40) = 72 inches. Since the three shelves are equally spaced then that that means the third shelve is the mid-segment of the trapezoid of shelves. The mid-segment is half of the sum of the other two bases which in this case is 36. 72 in. + 36 in. = 108 inches.