Question

The dimensions of a rectangular box are in the ratio 4: 2 : 3. The difference between the cost of covering it with paper at Rs. 12 per m² and with paper at the rate of 13.50 per m² is Rs. 1,248. Find the dimensions of the box. 

Answer 1

Given dimensions of a rectangular box are in the ratio 4: 2 : 3
Therefore, the total surface area of the box = 2`[ 4x xx 2x + 3x + 4 xx 3x ]`
 = 2 ( 8x² + 6x² + 12x² ) m² 

Difference between cost of  covering the box with paper at Rs. 12 per m² and with paper at Rs. 13.50 per m² = Rs. 1,248 
⇒ 52x²[ 13 .5 - 12 ] = 1248
⇒ `52 xx x^2 xx 1 . 5` = 1248
⇒ 78 x x² = 1248 
⇒ x² = `( 1248)/( 78)`
⇒ x² = 16 
⇒ x = 4             ...[ length, width and height cannot be negative ]

Thus, the domensions of the rectungular box are : 4 x 4 m,  2 x 4 m, 3 x 4 m
Thus, the dimensions are 16 m, 8 m aand 12 m.