Question

the Length breadth and height of a solid cuboid are in the ratio 5:4:2 if the TSA is 1216 find the dimensions of the cuboid

Answer 1

Let the length, breadth and height of the cuboid be 5x, 4x and 2x, respectively.

The total surface area of the cuboid is 2(LB +BH +HL) = 1216, or

(LB +BH +HL) = 608, or

(20x^2 + 8x^2 + 10x^2) = 608, or

38x^2 = 608, or

x^2 = 608/38 = 16, or x = 4.

The dimensions of the cuboid are 20 cm x 16 cm x 8 cm and so its volume = 2560 cc.

If uh don't get this properly, refer to the answer below, it's somewhat the same:

Let R represent the unknown.

To maintain the 5:4:2 ratio the sides are (5R x 4R), (5R x 2R) & (2R x 4R)

Surface area is sum of the area of the 6 surfaces.

The surface area = 2 ((20R^2) + (10R^2) + (8R^2)) = 2(38R^2) = 76R^2 = 1,216

R^2 = 1,216/76 = 16

R = 4

Dimensions are 5R, 4R & 2R or 20, 16 & 8.

Volume is 20*16*8 = 2,560 cubic cm.

Hope This Helps :)