Question

An open box is made from a 20 cm x 3 cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is 96 cm². What is the length of the sides of the squares.

Answer 1

Answer:

Length of the final sides: 6 cm and 16 cm

Step-by-step explanation:

The lengths of the sides of the original box are

$L=20 cm\\W=10 cm$

Later, a piece of tin is cut out from each corner; the piece cut out has the shape of the square: we can call the length of its generic side x. Therefore, the dimensions of the box will now be:

$L'=L-2x\\W'=W-2x$

We also know that the area is

$A=96 cm^2$

And the area can be written as product of length and width, therefore:

$A=L'W'$

So we find:

$A=(L-2x)(W-2x)\\96=(20-2x)(10-2x)$

Solving for x,

$96=200-20x-40x+4x^2\\4x^2-60x+104=0\\\\x^2-15x-26=0$

Which has two solutions:

x = 13 cm (this is larger than the initial length of the width, therefore we discard it)

x = 2 cm

So, the length of the new sides are

$L=20-2x=20-2(2)=16 cm\\W=10-2x=10-2(2)=6 cm$