# The Length, Breadth and Height of a Cuboid Are in the Ratio 5:4: 2. If the Total Surface Area is 1216 Cm2, Find Dimensions of the Solid. - Geometry

Sum

The length, breadth, and height of a cuboid are in the ratio 5:4: 2. If the total surface area is 1216 cm2, find dimensions of the solid.

#### Solution

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

Total Surface Area(TSA) = (LB+BH+LH) =1216

(LB+BH+LH) = 608

[(5x × 4x) +(4x × 2x) +(5x × 2x) =608

[20x2 +8x2+10x2] =608

38x2 = 608

x2 = 608/38

x2 = 16

x = 4

The dimension of the cuboid is:

Length = 5x = 5(4) = 20cm

Breadth = 4x = 4(4) = 16cm

Height = 2x = 2(4) = 8cm

volume = (L×B×H)

Volume = 20 × 16 × 8

Volume = 2560cm2

Concept: Surface Area of a Combination of Solids
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