Question

The sum of the lengths of the twelve edges of a rectangular box is $140$, and the distance from one corner of the box to the farthest corner is $21$. The total surface area of the box is

• A. $784$
• B. $800$
• C. $798$
• D. $776$

Answer 1

Answer: (A)

sum of length of $\frac{h}{2}$ edges

$=4(l+b+h)=140$

$\Rightarrow l+b+h=35$........(1)

Also, length of largest body diagonal of a cuboid is give as $21$

$\sqrt{l^2+b^2+h^2}=21$

$\Rightarrow l^2+b^2+h^2=(21{)}^2$

Now, we have to find the total surface area of the box .

Total surface are $=2(lb+bh+lh)$

And, for $(l+b+h{)}^2=l^2+b^2+h^2+2lb+2bh+lh$

$(35{)}^2=(21{)}^2+2(lb+bh+lh)$

$1225=441+2(lb+bh+lh)$

$2(lb+bh+lh)=784$

Hence, the total surface area of box is $784$ sq. units