Question

The ratio of length, width and height of a room is 8: 6: 5. If the length, width and height of the room are each increased by 1 meter, the area of ​​the walls will be 1408 square meters. Remove the length, width and height of the room.​

Answer 1

Given :

The ratio of length , width and height of room = 8 : 6 : 5

If the length, width and height of the room are each increased by 1 meter, the area of ​​the walls will be 1408 square meters

To Find :

The length , width and height of the room

Solution :

Let The length of room = 8 x  meters

The width of room = 6 x   meters

The height of room = 5 x  meters

∵  The  length, width and height of the room are each increased by 1 meter

Then ,

The length of room = ( 8 x + 1 )  meters

The width of room = ( 6 x + 1 )  meters

The height of room = ( 5 x + 1 )  meters

Again

∵  Area of four wall = 2 × ( length + width ) × height

                                 = 2 × [ ( 8 x + 1 ) +  ( 6 x + 1 ) ] ×  ( 5 x + 1 )

Or,  2 × [ ( 8 x + 1 ) +  ( 6 x + 1 ) ] ×  ( 5 x + 1 ) = 1408

Or,  2 ×  ( 14 x + 2 ) ] ×  ( 5 x + 1 ) = 1408

Or,  2 × ( 70 x² + 24 x + 2 ) = 1408

Or, ( 70 x² + 24 x + 2 ) = $\dfrac{1408}{2}$

or, ( 70 x² + 24 x + 2 ) = 704

Or, ( 70 x² +24 x- 702 ) = 0

Solving this quadratic eq

x = $\dfrac{-24\pm \sqrt{(24)^{2}-4\times 70\times (-702)}}{2 \times 70}$

Or,  x = 3 , -3.3

Now,

Put the value of x

The length of room = 8 x = 8 ×3  = 24 meters

The width of room = 6 x = 6 ×3  =  18 meters

The height of room = 5 x = 5 ×3  = 15 meters

Hence,

The length of room is 24 meters

The width of room is 18 meters

The height of room is 15 meters   Answer