The length of the longest rod which can, be kept inside a rectangular box is 27 cm. If the length and the breadth of the box are 23 cm and 10 cm respectively, find its height.
Answer & explanation
Correct answer: option 2
Given that the length of the longest rod = 27 cm.
Length of the box, l = 23 cm
Breadth of the box, b = 10 cm.
Let ‘h’ be the height of the box length of the longest rod
= Length of the diagonal = $\sqrt{l^2+b^2+h^2}⇒24=\sqrt{(23)^2+(10)^2+h^2}$
Squaring on both sides ⇒ $(27)^2=(23)^2+(10)^2+h⇒h=\sqrt{100}=10$
Hence, the height of the box = 10 cm