The length, the breadth, and the height of a closed cardboard box are in the ratio of 5 : 3 : 7, respectively. Find the length of this box, if its total surface area is 1278 cm2.
Answer & explanation
Correct answer: option 2
We know that,
Total Surface area of cardboard box = 2(lb + bh +hl)
We have,
length, width and height ratio = 5 : 3 : 7
Total Surface area = 1278 cm2
Let, length = 5x
width = 3x
height = 7x
Total Surface area of cardboard box = 2(5x × 3x + 3x × 7x + 7x × 5x) = 1278 cm2
= 2(15x2 + 21x2 + 35x2) = 1278 cm2
= (71x2) = 639
= x2 = 9
= x = 3
Length of the box = 5 × 3 = 15cm