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What is the entire surface area of a right angle triangular prism whose height is in the ratio of 4 to 3 to its width and has a length of 15 cm with a volume of 585.225 cubic cm showing all work?
Wiki User
∙ 10y ago
1 Let the height and width be 4x and 3x respectively
2 So: 0.5*4x*3x*15 = 585.225 => 90x2 = 585.225
3 Divide both sides by 90 and then square root each side
4 Therefore: x = 2.55 so height = 4*2.55 = 10.2 cm, width = 3*2.55 = 7.65 cm
5 Hypotenuse: 5*2.55 = 12.75 cm because it's part of a Pythagorean triple
6 Area: 2*(0.5*10.2*7.65)+(15*12.75)+(15*10.2)+(15*7.65) = 537.03 cm2
7 Check: 0.5*10.2*7.65*15 = 585.225 cubic cm
Wiki User
∙ 10y ago
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