Sum of sides in a Cuboid

Question

So, I came across this question:

What is the value of surface area of the cuboid $C$ ?
(1) The length of the diagonal of $C$ is $5$
(2) The sum of the sides of $C$ is $10$

Now, if we take the dimensions of cuboid $C$ as $\ell, b$, and $h$, the second condition should be expressed as $4(\ell+b+h)=10$. However, the official answer expresses it simply as $\ell+b+h=10$. Doesn't a cuboid have $12$ sides(edges)?

Can someone shed some light on this.

Answer 1

i dont understand what do you mean by "Can someone shed some light on this."

.....Now considering the problem here

What is the surface area of the cuboid C ?

(1) The length of the diagonal of C is 5

(2) The sum of the sides of C is 10

from .....(1)

l^2+b^2+c^2=25...... draw the figure and apply pythagorous theorem

from .....(2)

• l+b+h=10 ...........OR as you thought
• 4{l+b+h}=10

you should know this

                     (a + b + c)^2 = (a + x)^2 = a^2 + 2ax + x^2

                     = a^2 + 2a (b + c) + (b + c)^2 

                     = a^2 + 2ab + 2ac + (b^2 + c^2 + 2bc) 

                     = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

now think a=l,b=b,c=h

now you should solve the problem......out of the two cases from {2}

IN the first case you will get a answer of 75/2

and in the second case you will get a negative value....

so you know which answer to choose