Mathematics

The volume of a cuboid is 3600 cm³ and its height is 12 cm. The cross-section is a rectangle whose length and breadth are in the ratio 4 : 3. Find the perimeter of the cross-section.

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Given,

Volume of a cuboid = 3600 cm³

Height of cuboid = 12 cm

Cross section is a rectangle with length and breadth in ratio 4 : 3.

Let length = 4x cm and breadth = 3x cm.

By formula,

Volume of cuboid = length × breadth × height

⇒ 3600 = 4x × 3x × 12

⇒ 144x² = 3600

⇒ x² = $\dfrac{3600}{144}$

⇒ x² = 25

⇒ x = $\sqrt{25}$ = 5 cm.

So.

Length of rectangle = 4x = 4 × 5 = 20 cm

Breadth of rectangle = 3x = 3 × 5 = 15 cm

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

= 2(20 + 15)

= 2 × 35

= 70 cm.

Hence, perimeter of cross-section = 70 cm.

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