1. ## Problem solving with quadratics

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 $\displaystyle x$ and the height is $\displaystyle x+1$

From the information given,

$\displaystyle 240 = 6x^2+ 4x$

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

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

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

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### if the sum of three dimensions and the total surface area of a rectangular box is 12 cm and 96cm^2 reap. then the max length of a stick that can be placed inside the box is

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