Question

The box is laid on its side and the white label covers 75% of the lateral surface area of the box. Find the length x of the box.

The box is laid on its side and the white label covers 75% of the lateral surface area of the box. Find the length x of the box.

Answer 1

x = 7.7 inches

Explanation:

75% of the lateral surface area of the box = Area of the sticker

Area of the sticker = 2(length + width) × height

= 2(5 + 4.5)(1)

= 19 square inches

75% of the lateral surface area of the box = 19 square inches

`(75)/(100)(L.S.A.) = 19`

L.S.A. of the box =
`(19)/(0.75)`

= 25.33 square inches

Since lateral surface area of the rectangular box = 2(l + b)h

= 2(x + 5)(1)

Therefore, 2(x + 5) = 25.33

x + 5 = 12.67

x = 12.67 - 5

x = 7.67

x ≈ 7.7 inches

Therefore, length of x is 7.7 inches.