Question

the ratio of length breadth and height of a room is 4 : 2 : 1 . If the total surface area is 2800m^2. Find the dimension of the room​

Answer 1

Given:-

• Ratio of length breadth and height of a room is 4 : 2 : 1
• TSA = 2800 m²

To FInd :-

Dimension of the room​

Solution :-

Let,

$\bf Length=4x$

$\bf Breadth =2x$

$\bf Height=x$

Now

We know that

${\boxed{\bf{TSA\;of\;cuboid=2(lb+bh+lh)}}}$

$\sf \implies 2800=2(4x\times 2x+2x\times x+4x\times x)$

$\sf \implies 2800=2(8x^2+2x^2+4x^2)$

$\sf \implies 2800=2(14x^2)$

$\sf \implies 2800=28x^2$

$\sf \implies\dfrac{2800}{28}=x^2$

$\sf \implies 100=x^2$

$\sf \implies \sqrt{100}=x$

$\sf \implies 10=x$

Dimensions of room are

Length = 4x = 4(10) = 40 m

Breadth = 2x = 2(10) = 20 m

Height = x = 10 m