Question 519560
Let the length of the sides of the square = x.
Then the dimensions of the base of the constructed box will be:
{{{(x-10)}}} by {{{(x-10)}}} and its height will be 5.
You can express the volume of the constructed box by:
{{{V = (x-10)(x-10)*5}}} Substitute {{{V = 125}}} as the desired volume of the box.
{{{125 = (x-10)(x-10)*5}}} After simplifying, rearrange into a standard-form quadratic equation.
{{{x^2-20x-25 = 0}}} Do you see how we got this? Solve using the quadratic formula: {{{x = (-b+-sqrt(b^2-4ac))/2a}}}:
{{{x = (-(-20)+-sqrt((-20)^2-4(1)(-25)))/2(1)}}} You can work this out using your calculator. You'll get two answers only one of which will be valid.
{{{x = 10+5*sqrt(5)}}} or {{{10-5*sqrt(5)}}} These are the "exact" answers.
{{{x = 21.1803398875}}} or {{{x = -1.1803398875}}} Discard the negative solution as the length of the side can only be a positive value.
So the original sheet metal square is 21.2 inches (approx.) on each side.