SOLUTION: I need help with this problem please: I found it on here but it is worded wrong. Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilze the d

Question 205907: I need help with this problem please: I found it on here but it is worded wrong.
Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilze the door by attaching a steel cable diagonally. If the cable measures sqrt194/2ft, what are the dimensions of the door?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilze the door by attaching a steel cable diagonally. If the cable measures sqrt194/2ft, what are the dimensions of the door?
.
Let w = width of door
then
w+4 = length of door
.
From Pythagorean theorem we know:

Applying the quadratic equation we get:
w = {3.153, -5.153}
Throwing out the negative solution we're left with:
w = 3.153 feet (width)
.
Length:
w+4 = 3.153 + 4 = 7.153 feet (length)
.
Details of quadratic:

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=1104 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.15331193145904, -5.15331193145904. Here's your graph:

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