question 1: A rectangular box has a square base and its height is 1 cm longer than the length of one side of its base.
the total surface area is given by
A= 6X^2+ 4X

If the total surface area is 240 cm^2, find the dimensions of the box.

Question 2: An open box contains 80 cm^3 and is made from a square piece of tinplate with 3 cm squares cut from each of its 4 corners. Find the dimensions of the original piece of tinplate.

Question 3: Is it possible to bend a 20 cm length of wire into the shape of a rectangle which has an area of 30 cm^2?

2. Originally Posted by Tessarina
question 1: A rectangular box has a square base and its height is 1 cm longer than the length of one side of its base.
the total surface area is given by
A= 6X^2+ 4X

If the total surface area is 240 cm^2, find the dimensions of the box.

Lets say the width and length of the square base is $x$ and the height is $x+1$

From the information given,

$240 = 6x^2+ 4x$

$0 = 6x^2+ 4x- 240$

$0 = 3x^2+ 2x- 120$

Now find $x$ using the quadratic formula, disgard any negative values.