Aptitude Discussion

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

✖ A. |
40 |

✖ B. |
50 |

✔ C. |
60 |

✖ D. |
80 |

**Solution:**

Option(**C**) is correct

In the figure above,

The areas of the three sides are given by \(HW, HL,\) and \(LW\).

Assuming \(HW=12 = (3)(4), HL = 15 = (3)(5),\) and

\(LW= 20 = (5)(4),\)

it is clear that possible choices for the edge lengths are

\(H= 3, W=4, \)and \(L =5\)

Therefore, the volume of the rectangular solid is

\(=(3)(4)(5) \)

\(=60\)

**Edit:** For an *alternative method* (and a good one), kindly check **KARTIK's comment.**

**Smit**

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**KARTIK**

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we know

volume of cuboid is $= LBH$

here we have $LB$, $BH$, $HL$

so if we multiply them $= LB \times BH \times LH=(LBH)^2$

Root of above would give the ans.

(if u have trouble searching possible choices)

This is an awesome alternative solution, for those who are wondering how to calculate root vale, here is my take:

$\Rightarrow LB \times BH \times LH=(LBH)^2$

$=(\text{Volume})^2= (12) \times (15) \times (20)$

$\Rightarrow \text{Volume} = \sqrt{(4 \times 3)(5 \times 3)\times (4 \times 5)}$

$\Rightarrow \text{Volume}= 3 \times 4 \times 5$

$\Rightarrow \text{Volume}= \textbf{60}$

We can simply take LCM of areas of all side i.e LCM(12,15,20)=60