Equation

You are instructed to make an open box from a piece of cardboard that is 60 cm on each side.
The bottom of the box must have an area of 3,100 sq cm. How high will the sides t be?

t = height of sides
3,100 sq cm = (60 - 2t)(60 - 2t)
3,100 = 3600 - 240t + 4t²
0 = 3600 - 3,100 - 240t + 4t²
0 = 500 - 240t + 4t²
Divide both sides by 4
0 = 125 - 60t + t²

Use the quadratic formulae and t = 57.8 cm or t = 2.16 cm

60 - 2t = 60 - 2(57.8) = -55.68 You cannot have a negative length and hence this answer 57.8 is impossible.
60 - 2t = 60 - 2(2.16) = 55.68 which when square will approximately equal 3,100
so t = approximately 2.16 cm
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