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galina1969 [7]
3 years ago
10

A rectangular solid has edges whose lengths are in the ratio 1:2:3. If the volume of the solid is 864 cubic units, what are the

lengths of the solid's edges?
Mathematics
1 answer:
andrew-mc [135]3 years ago
3 0

Answer: 5.24 units, 10.48 units , 15.72  units

Step-by-step explanation:

Volume of a rectangular solid is given by :-

V = lwh, where l = length , w= width and h = height

Given: A rectangular solid has edges whose lengths are in the ratio 1:2:3.

Let lengths of the rectangular solid x , 2 x, 3x.

volume of the solid is 864 cubic units

Then, Volume of rectangle = x (2x)(3x) =864\ \text{cubic units}

\Rightarrow\ 6x^3 = 864\\\\\Rightarrow\ x^3 =144\\\\\Rightarrow\ x=(144)^{\frac{-1}{3}}\approx5.24

Lengths of rectangular solid 5.24 units, 2 (5.24) units , 3(5.24) units

= 5.24 units, 10.48 units , 15.72  units

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