Question

The top of a rectangular box has an area of 42 cm?. The sides have areas of 48 cm? and 56 cm? What are the dimensions of the box?

Answer 1

The dimensions of the rectangular box are l, w, h

l is the length

w is the width

h is the height

The dimensions of the base and the top are l and w

The dimensions of the sides are l, h, and w, h

Since the area of the top is 42 cm^2, then

$l\times w=42$

Since the area of the sides are

48 cm^2 and 56 cm^2, then

$\begin{gathered} l\times h=48 \\ w\times h=56 \end{gathered}$

Since h is a common between 48 and 56, then

Let us find the products of two numbers give 48 and 56

$\begin{gathered} 48=6\times8 \\ 56=7\times8 \end{gathered}$

Then h must be equal to 8

Since 42 is the product of

$42=6\times7$

Then the length and the width are 6 and 7

$\begin{gathered} l=6 \\ w=7 \\ h=8 \end{gathered}$

The dimensions of the box are

6 cm, 7 cm, 8 cm