Question

the length,breadth,and height of a rectengular solid are in ratio of 5:4:2 .if the tsa is 1216 cm,find the length,breadth and height of a solid

Answer 1

Ratio of Length : Breadth : Height = 5 : 4 : 2

Define x:

Let x be the constant ratio

Ratio of Length : Breadth : Height = 5x : 4x : 2x

Form equation:

Total surface area = 2 ( Length x Breadth + Length x Height + Breadth x Height)

1216 = 2 ( (5x)(4x) + (5x)(2x)+ (4x)(2x) )

1216 = 2 (20x² + 10x² + 8x² )

1216 = 2 (38x² )

1216 = 76x²

x² = 16

x = √16

x = 4

Find the dimension:

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

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

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

Answer: Length = 20 cm, breadth = 16 cm and height = 8 cm

Answer 2

let lenth of all sides=x
so, length=5x
breadth=4x
height=2x
Now,tsa of cuboid=2(lb+bh+lh)
so, 2((5x*4x)+(4x*2x)+(5x*2x))=1216
$2(20 {x}^{2} + 8 {x}^{2} + 10 {x}^{2} ) = 1216 {cm}^{2}$
$76 {x}^{2} = 1216 {cm}^{2}$
${x}^{2} = 1216 \div 76$
${x}^{2} = 16 \\ x = 4cm$
so, length=20cm
bredth=16cm
height=8cm
Hope it will help you...