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

21 m, 10 m, 12 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

21 m, 15 m, 12 m

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

26 m, 15 m, 12 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 m, 5 m, 12 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $21 m, 15 m, 12 m$
Let length, breadth and height are respectively $l, b, h = 7 x, 5 x, 4 x$
$4$ walled area $= 2 h (l + b)$
$= 2 \times 4 x (7 x + 5 x) = 96 x^{2}$

When dimensions changed $7 x + 1, 5 x + 1, 4 x + 1$

New Area $= 2 \times (4 x + 1) (7 x + 1 + 5 x + 1) = 96 x^{2} + 124$
$\Rightarrow 96 x^{2} + 24 x + 16 x + 4 = 96 x^{2} + 124$

$40 x = 120 \Rightarrow x = 3$

Length, breadth and height are respectively $l, b, h = 21 m, 15 m, 12 m .$

Hence, this is the answer.

Suggest Corrections

Similar questions

12 m, 15 m

18 m

12 m

21 m

15 m

12 m

2 m

10 \sqrt{5} m

Join BYJU'S Learning Program