Question

Ratio of length and breadth and height of a room is 5:4:2. Area of four wall is 144. Find the diagnonal of the room

Answer 1

find diagonals or dimensions?

Answer 2

Answer:

√164 or 2√41 meters.

Step-by-step explanation:

Let us consider x as a constant.

Given that the length, breadth, and height are 5x, 4x, 2x, respectively.

Area of four wall is 144 square meters, i.e., Lateral Surface Area (LSA) is 144 square meters.

LSA=144m

2h( l + b )=144 Since, LSA of a Cuboid is 2h( l + b ).

2(2x)(5x+4x)=144

4x(9x)=144

36x^2=144

So, x=2.

By placing the value of x in the ratio values 5x, 4x, 2x, we get the values as follows:

length = 5x = 5(2) = 10

breadth = 4x = 4(2) = 8

height = 2x = 2(2) = 4.

Now, for finding the diagonal of the floor, we use Pythagoras theorem:

d^2 = 10^2 + 8^2

d = √164 or d = 2√41.