Question

the lateral surface area of cuboid is 300cm square. the length, breath and height are in the ratio 4:2:1. find the length, breath and height of the cuboid.

Answer 1

here is your answer

Answer 2

SOLUTION :

The lateral surface area of a cuboid = 300 cm sq.   (given)

The length, breadth and height are in ratio = 4:2:1 respectively   (given)

To be found :-

The length, breadth and height of the cuboid

Let,

Length be 4x cm

breadth be 2x cm

height be 1x cm

We know that,

Lateral Surface Area (LSA) of a cuboid = 2h(l + b)  unit sq.

[ In which l is the length, b is the breadth and h is the height of the cuboid ]

⇒ 2h(l + b) = 300

⇒ 2 × 1x (4x + 2x) = 300

⇒ 2x (4x + 2x) = 300

⇒ 8x + 4x = 300

⇒ 12x = 300

⇒ x = 300 ÷ 12

⇒ x = 25

∴ The value of x is 25 cm

Now,

Length be 4x cm = 4 × 25 = 100 cm

breadth be 2x cm = 2 × 25 = 50 cm

height be 1x cm = 1 × 25 = 25 cm

Hence,

The length of the cuboid is 100 cm

The breadth of the cuboid is 50 cm

And the height of the cuboid is 25 cm