Question

The length and breadth of a cuboid are in the ratio of 5 : 7 ; whereas its height is 8cm and lateral surface area is 3072cm². Find it's length and breadth.​

Answer 1

Answer:

If the length and breadth of the cuboid are in the ratio 5:7 and its height is 8 cm, then if the lateral surface area of the cuboid is 3072$cm^{2}$, its length and breadth are 80 cm and 112 cm respectively.

Step-by-step explanation:

Given

The ratio of length to breadth of the cuboid = 5:7

That is if the length of the cuboid is 5x, then its breadth is 7x

Also given,

Height of the cuboid = 8 cm

The lateral surface area of the cuboid = 3072$cm^{2}$

The lateral surface area of the cuboid = 2(lh+ bh)

Here, l= 5x

b = 7x

h = 8 cm

Lateral surface area = 3072$cm^{2}$

Then, 3072$cm^{2}$ =

$2[(5x*8)+(7x*8)]\\\\\frac{3072}{2} = 40x + 56x\\\\1536 = 96x\\\\x =\frac{1536}{96} = 16$

Then l= 5x = 5*16 = 80cm

b= 7x = 7*16 = 112cm

Therefore the length and breadth of the cuboid are 80cm and 112cm respectively