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1 Let its height be 12x and its width be 5x

2 So: 0.5*12x*5x*40 = 7500 or 1200x2 = 7500 cm3

3 Divide both sides by 1200 and then square root both sides

4 Therefore: x = 2.5 so height is 12*2.5 = 30 cm and width is 5*2.5 = 12.5 cm

5 Hypotenuse: 13*2.5 = 32.5 cm because it's a Pythagorean triple

6 Area: (2*0.5*30*12.5)+(30*40)+(12.5*40)+(32.5*40) = 3375 cm2

7 Check: 0.5*30*12.5*40 - 7500 cubic cm

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Q: What is the surface area of a right angle triangular prism whose height is in the ratio 12 to 5 to its width with a length of 40 cm and a volume of 7500 cubic cm showing work?
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