Question

the sum of length breadth and height of a cuboid is 25 cm and the length of its diagonal is 15 cm find the total surface area of a cuboid​

Answer 1

l+b+h=25 And l2+b2+h2 in under root=15(both sides squaring)

=l2+b2+h2=225..........1

l+b+h=25(both sides squaring)

l2+b2+h2+2(lb+bh+hl)=625

225+2(lb+bh+hl)=625

2(lb+bh+hl)=625-225

=400

Answer 2

$\huge\mathfrak{Answer-}$

Given ;-

Lenght + Breadth + Height of a cuboid = 25 cm.

Lenght of the diagonal of the cuboid = 15 cm.

To find the Total Surface Area ;-

$= > \sqrt{(l^{2} + {b}^{2} + {h}^{2} )} = 15$

Squaring on Both the Sides.

$= > {l}^{2} {b}^{2} { h}^{2} = {15}^{2}$

Now ,

$= > ( {l}^{2} {b}^{2} {h}^{2} ) - 2(lb + bh + hl) = 225$

$= > {25}^{2} - 225 = 2(lb + bh + lh)$

$= > 625 - 225 = surface \: area$

$= > surface \: area \: = 400 \: cm^{2}$

Therefore ,

The Total Surface Area of the given Cuboid = 400 cm^2