Question

the length, breadth and height of a room are in a ratio 5:4:3 and the length of its dialogical is 10√2 m. finds the total area of 4 walls and the ceiling​

Answer 1

Answer:

the length, breadth and height of a room are in a ratio 5:4:3 and the length of its dialogical is 10√2 m. finds the total area of 4 walls and the ceiling

Answer 2

Answer:

296 m²

Step-by-step explanation:

Given:

• Length, Breadth and Height are in ratio 5 : 4 : 3
• Length of its diagonal = 10√2 m

To find:

• Total Area of 4 walls & ceiling

Solution:

Let length, breadth & height of the room be 5x, 4x & 3x respectively

Since all 3 are different, we consider the room to be in cuboidal shape

$diagonal \: of \: cuboid \: is \: given \: by \\ \sqrt{ {l}^{2} + {b}^{2} + {h}^{2} }$

where,

• l = length of the cuboid
• b = breadth of the cuboid
• h = height of the cuboid

Here,

• l = 5x
• b = 4x
• h = 3x

Diagonal = 10√2 m

Using the formula, we get

$10 \sqrt{2} = \sqrt{( {5x})^{2} + ( {4x})^{2} + ({3x})^{2} }$

$10 \sqrt{2} = \sqrt{25 {x}^{2} + 16 {x}^{2} + 9 {x}^{2} }$

$10 \sqrt{2} = \sqrt{50 {x}^{2} }$

Squaring on both sides, we get

$( {10 \sqrt{2} })^{2} = 50 {x}^{2}$

$200 = 50 {x}^{2}$

${x}^{2} = 4$

$x = 2$

Length ( l ) = 5(2) = 10 m

Breadth ( b ) = 4(2) = 8 m

Height ( h ) = 3(2) = 6 m

Area of four walls = 2 ( lh + bh )

=> 2 ( (10*6) + (8*6) )

=> 2 ( 60 + 48 )

=> 2 ( 108 )

= 216 m²

Area of ceiling = lb

=> 10*8

= 80 m²

Total Area = 216 + 80 = 296 m²