In the rectangular solid above, the three

In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

2 Explanations

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Bradley S Erla

I answered this by finding the LCM of the three numbers:
12 = 2*2*3
15 = 3*5
20 = 2*2*5

LCM = 2*2*3*5 = 60

Will this work every time we are given the area of the three sides of rectangular solid?

Nov 25, 2015 • Comment

Cydney Seigerman, Magoosh Tutor

Great question! If the sides of the rectangular solid are integers, then yes, the method you've described will get you to the correct answer. However, and as Mike mentions in his explanation, you could be given a question like but this with values with decimals. Since the LCM refers to integers, you could not use your method if the areas were expressed in non-integer values. To solve a question like this one, I recommend using the approach Mike explains: since the product of the three areas is the volume squared, we can find the volume of the rectangular solid by finding the square root of that product.

Nov 29, 2015 • Reply

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Mike McGarry, Magoosh Tutor