Question

find the diagonal of cuboid of length 25 CM breadth 20 cm and height 15 CM

Answer 1

From the figure attached with this answer, we can see that

cuboid of length AB =25 CM breadth BC = 20 cm and height CD=15 CM

AC is the base diagonal  and AD is the cuboid diagonal.

to find the diagonal of cuboid we need to find the base diagonal AC,

ΔABC is a right angled triangle with AC hypotenuse , so

AC =  $\sqrt{AB^{2}+ BC^{2}}$

= $\sqrt{625 + 400}$  

=$\sqrt{1025}$

ΔACD is a right angled triangle with AD hypotenuse

AD = [$\sqrt{AC^{2}+CD^{2}}$

    = $\sqrt{1025 + 225}$  =$\sqrt{1250}$

    =25√2 cm

Answer 2

Formula to find the diagonal of a cuboid :

$\text {Diagonal} = \sqrt{Length^2 + Breadth^2 + Height^2}$

Apply the formula:

Length = 25 cm

Breadth = 20 cm

Height = 15 cm

$\text {Diagonal} = \sqrt{25^2 + 20^2 + 15^2}$

$\text {Diagonal} = \sqrt{625 + 400 + 225}$

$\text {Diagonal} = \sqrt{1250}$

$\text {Diagonal} = 25\sqrt{2}$

Answer: The diagonal is 25√2 cm