SOLUTION: boris has a rock garden in the shape trapezoid. The garden has an area of 90m2 and a depth of 12m. The front width is 4 times the length of the back width. Without changing the fro

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Question 1002027: boris has a rock garden in the shape trapezoid. The garden has an area of 90m2 and a depth of 12m. The front width is 4 times the length of the back width. Without changing the front and back widths, by how much must Boris increase the depth of his garden to triple the area?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Two bases are here called "widths". One base is some x and the other width base is 4x.

Initial area is %28%284x%2Bx%29%2F2%29%2A12=90
5x%286%29=90
30x=90
highlight%28x=3%29

Triple the area keeping the same two bases' measures.
d is for variable depth.
3%2A90=270, the tripled area.
-
%28%284%2A3%2B3%29%2F2%29%2Ad=270
%2815%2F2%29d=270
d=270%282%2F15%29
highlight%28d=36%29-----the new depth.