Question

The length, breadth and height of a rectangular box are in the ratio of 4:3:2. the total surface area of the box is 2548cm square. find the length breadth and height​

Answer 1

The length , breadth and height are length = 28cm , breadth = 21 cm and height = 14 cm.

• The length , breadth and height of the rectangular box are in the ratio 4:3:2.
• Let us assume the common multiple of the ratios be x.
• The length(l) becomes 4x , breath(b) becomes 3x and the height(h) becomes 2x.
• Now the total surface area of the rectangular box is given as 2548 cm².
• Total surface area =2(lb + bh +hl)

• Substituting the values in the formula,

TSF = $2(12x^2 + 6x^2 + 8x^2)$

2548 = $2(12x^2 + 6x^2 + 8x^2)$

2548 = $2(26x^2)$

1274 = $26x^2$

49 = $x^2$

x = 7.

• Therefore, length = 28cm , breadth = 21 cm and height = 14 cm.