SOLUTION: There is a rectangle with 2 diagonals. The diagonals are RT and QS with intersection C. The problem gives you RT as 3xsquared and QC as 5x+4. Thye want you to find the value of x

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Question 171781This question is from textbook Geometry: Integration, Application and Connections
: There is a rectangle with 2 diagonals. The diagonals are RT and QS with intersection C. The problem gives you RT as 3xsquared and QC as 5x+4. Thye want you to find the value of x. This question is from textbook Geometry: Integration, Application and Connections

Found 2 solutions by nerdybill, Earlsdon:
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
Since the diagonals are equal, this means RT = QC
.
3x^2 = 5x+4
3x^2 - 5x - 4 = 0
.
Since you can't factor you must resort to the quadratic equation. Doing so will yield the following solutions:
x = {2.257, -0.591}
.
You can toss out the negative solution leaving:
x = 2.257
.
Details of quadratic follows:
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=73 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2.25733395755292, -0.590667290886255. Here's your graph:

(3x+2)(x-2) = 0
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
My appologies to Nerdy Bill but the solution is a bit off.
From the description of the rectangle and its diagonals, the one diagonal is but the other diagonal QS is really given as and this is but half of the complete diagonal QS, so the equation becomes:
or
Rewriting this it becomes:
...and this is factorable to:
and so...
or and, as you pointed out, you can discard the negative quantity as we are talking about lengths, so...
x = 4
Check:
=
=
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