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

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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) About Me  (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:
+w%5E2+%2B+%28w%2B4%29%5E2+=+%28sqrt%28194%29%2F2%29%5E2+
+w%5E2+%2B+%28w%5E2%2B8w%2B16%29+=+194%2F4+
+2w%5E2+%2B+8w+%2B+16++=+194%2F4+
+8w%5E2+%2B+16w+%2B+64++=+194+
+8w%5E2+%2B+16w+-+130++=+0+
+4w%5E2+%2B+8w+-+65+=+0+
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 aw%5E2%2Bbw%2Bc=0 (in our case 4w%5E2%2B8w%2B-65+=+0) has the following solutons:

w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%288%29%5E2-4%2A4%2A-65=1104.

Discriminant d=1104 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+1104+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%288%29%2Bsqrt%28+1104+%29%29%2F2%5C4+=+3.15331193145904
w%5B2%5D+=+%28-%288%29-sqrt%28+1104+%29%29%2F2%5C4+=+-5.15331193145904

Quadratic expression 4w%5E2%2B8w%2B-65 can be factored:
4w%5E2%2B8w%2B-65+=+4%28w-3.15331193145904%29%2A%28w--5.15331193145904%29
Again, the answer is: 3.15331193145904, -5.15331193145904. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B8%2Ax%2B-65+%29