Question

the length, breadth and height of a rectangular solid are on the radio 5:4:2. if the total surface area is 2736 cm²,find the dimensions of the solid​

Answer 1

Answer:

This is the answer, Hope it helps you..:)

Answer 2

Answer -

Let the ,

• Length of the cuboid = 5x
• Breadth of the cuboid = 4x
• Height of the cuboid = 2x

We know that

• Total surface area = 2736 cm²

To find

• The dimensions of the solid

Formula For Total surface area of a cuboid where ,

• length = l
• breadth = b
• height = h
• total surface area = tsa

$:\longrightarrow\boxed{\boxed{\rm{\red{tsa = 2lb + 2bh + 2lh}}}}$

$:\longrightarrow\boxed{\boxed{\rm{\red{tsa = 2(lb+bh+lh)}}}}$

Values ,

• l = 5x
• b = 4x
• h = 2x

Substituting the values, We get,

$\rm:\implies{\purple{2(5x \times 4x + 4x \times 2x+2x \times 5x)=2736 {cm}^{2} }}$

$\rm:\implies{\purple{2(20x + 8x+10x)=2736 {cm}^{2}}}$

$\rm:\implies{\purple{40x + 16x+20x=2736 {cm}^{2}}}$

$\rm:\implies{\purple{76x=2736{cm}^{2} }}$

$\rm:\implies{\purple{x= \sqrt{36} = \bold{6} }}$

Hence, the length of the cuboid

• length = 5x
• $\rm:\implies{\green{6 × 5 = 30 cm}}$

• breadth = 4x
• $\rm:\implies{\blue{4 × 6 = 24 cm}}$

• height = 2x
• $\rm:\implies{\pink{2 × 6 = 12 cm}}$