Atriangular prism is shown below. the base of the prism is a right triangle.

the volume of the prism is 720 cubic units. what is the product, in square units, of the width (x) and the height (y) of the prism.

a. 15

b. 30

c. 48

d. 60

The product is 60.

We start out with the information we have.  This forms a right triangle, with one leg being 24, the other leg x, and the hypotenuse 30.  Using the Pythagorean theorem we have

x²+24²=30²
x²+576=900

Subtract 576 from both sides:
x²+576-576 = 900-576
x²=324

Take the square root of each side:
√x²=√324
x=18

We know that the formula for the volume of a triangular prism is V=(1/2bh)H, where b is the base of the triangle, h is the height of the triangle, and H is the height of the prism. Substituting our known information we have:

720=(1/2*18*24)y
720=216y

Divide both sides by 216:
720/216 = 216y/216
3 1/3 = y

This means the product of x and y would be:
18(3 1/3)
18(10/3)
180/3
60

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