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Perimeter of a Triangle

The length, b...

Question

The length, breadth and height of a room are in the ratio $7 : 5 : 4$ . If each of them increases by $1$ m, the area of four walls increases by $124 m$ . Find the dimensions of the room.

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Solution

The length, breadth and height of a room are in the ratio $7 : 5 : 4$
Length $l = 7 x$
Breadth $b = 5 x$
Height $h = 4 x$

According to the given question,
Area of 4 walls $= 2 \times (l + b) \times h$
Initial Area
$A_{1} = 2 \times (7 x + 5 x) \times 4 x = 96 x^{2}$
New dimensions
Length $l = 7 x + 1$
Breadth $b = 5 x + 1$
Height $h = 4 x + 1$
New Area
$A_{2} = 2 \times (7 x + 1 + 5 x + 1) \times (4 x + 1) = 96 x^{2} + 124$

$96 x^{2} + 40 x + 4 = 96 x^{2} + 124$
$40 x = 120$
$x = 3$ ,
Hence, Dimensions of the room are
Length $l = 7 x = 21 m$
Breadth $b = 5 x = 15 m$
Height $h = 4 x = 12 m$

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