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

Answer:

x = 7.7 inches

Step-by-step 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

$\frac{75}{100}(L.S.A.) = 19$

L.S.A. of the box = $\frac{19}{0.75}$

                            = 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.