The volume of a cuboid is 14400 cm³ and its height is 15 cm. The cross-section of the cuboid is a rectangle having its sides in the ratio 5 : 3. Find the perimeter of the cross-section.

Given,

Volume of cuboid = 14400 cm³

Height = 15 cm

Given,

The cross-section of the cuboid is a rectangle having its sides in the ratio 5 : 3.

Let length = 5x and breadth = 3x.

We know that,

Volume of cuboid = l × b × h

⇒ 14400 = 5x × 3x × 15

⇒ 15x² = $\dfrac{14400}{15}$

⇒ 15x² = 960

⇒ x² = $\dfrac{960}{15}$

⇒ x² = 64

⇒ x = $\sqrt{64}$

⇒ x = 8.

∴ Sides of the rectangle :

⇒ Length = 5x = 5 × 8 = 40 cm.

⇒ Breadth = 3x = 3 × 8 = 24 cm

Perimeter of cross-section = 2(l + b)

= 2(40 + 24)

= 2(64)

= 128 cm.

Hence, perimeter of cross section = 128 cm.