SOLUTION: A rectangle is drawn so the width is 2 inches longer than the height. If the rectangle's diagonal measurement is 58 inches, find the height. Give your answer rounded to 1 decima

Question 930748: A rectangle is drawn so the width is 2 inches longer than the height. If the rectangle's diagonal measurement is 58 inches, find the height.
Give your answer rounded to 1 decimal place.
Answer by rcdodds(6) (Show Source): You can put this solution on YOUR website!
Well let's set this up as a system of equations.
Allow "w" to be the width.
Allow "h" to be the height.
Allow "d" to be the diagonal.
We know from the Pythagorean Theorem that...

but in this case

, so we can say that...
. Which is our first equation.
Our second equation comes from the "width is 2 inches longer than the height", which means that .
Substituting that into the first equation we can solve using algebra to find the height.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=6724 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 40, -42. Here's your graph:

Rounding this to one decimal place, we get our final answer to be 40 inches.
Note that we ignore the negative result from the quadratic formula because you can't have a negative distance.
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