# Moderate Geometry & Mensuration Solved QuestionAptitude 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.

## (3) Comment(s)

Smit
()

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

KARTIK
()

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)

Kriti
()

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

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

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

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

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

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