The volume of a rectangular parallelepiped is given as 144 cc. Its surface area is given as 192 sq cm. And its corner to corner diagonal is given as 13 cm. How do I find out the three sides.
I have assumed the sides to be $a,b,c$. Now, $a^2+b^2+c^2=169, 2(ab+bc+ca)=192$, and $abc=144$. How do I solve the three equations without forming a cubic equation? (This is a class 9 problem so i am not suppoesd to use solution to cubic equations.)
Best Answer
The quickest way is just to reacall pythagorean triples $(3,4,5)$ and $(5,12,13)$ due to 5 being common to both triples and 13 being the diagonal length thus establishing that 3, 4,and 12 satisfy $3^2+4^2+12^2=13^2$ as desired for the correct diagonal length. Notice that the product of these three numbers in the triples is 144 and they give the correct surface area.