SOLUTION: The diagonal of a rectangle is 10 inches and the area is 45 square inches. Find the dimensions of the triangle, correct to one decimal place.
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-> SOLUTION: The diagonal of a rectangle is 10 inches and the area is 45 square inches. Find the dimensions of the triangle, correct to one decimal place.
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Question 1040515: The diagonal of a rectangle is 10 inches and the area is 45 square inches. Find the dimensions of the triangle, correct to one decimal place. Found 2 solutions by rothauserc, ikleyn:Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! let l be length and w be width of the rectangle, then
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1) l^2 + w^2 = 10^2
2) l * w = 45
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we have two equations in two unknowns
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solve 2 for l and substitute in 1
l = 45/w
(45/w)^2 + w^2 = 100
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(2025/w^2) + w^2 = 100
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multiply both sides of = by w^2
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2025 + w^4 = 100w^2
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w^4 -100w^2 + 2045 = 0
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let u = w^2
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u^2 -100u + 2025 = 0
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use quadratic equation
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u = (100 + square root( (-100)^2 - 4(1)(2025) ) ) / 2 = 71.8
u = (100 - square root( (-100)^2 - 4(1)(2025) ) ) / 2 = 28.2
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since u = w^2, we have
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w^2 = 71.8 and w = 8.5
w^2 = 28.2 and w = 5.3
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we have 2 solutions for l as well
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l = 45/8.5 = 5.3
l = 45/5.3 = 8.5
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Our 2 solutions are
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w = 8.5 and l = 5.3
w = 5.3 and l = 8.5
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note that
8.5 * 5.3 = 45.05
8.5^2 + 5.3^2 = 100.34 and square root of 100.34 = 10.02
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