SOLUTION: I am having some trouble with this word problem, can some one help out and also show me the steps, thanks a lot Hazel has a screen door whose height is 4 feet more than its widt

Question 155442: I am having some trouble with this word problem, can some one help out and also show me the steps, thanks a lot
Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilize the door by attaching a steel cable diagonally. If the cable measures (Sqrt 194)/2 ft, what are the dimensions of the door?
A) 2 1/4 ft by 6 1/4 ft
B) 2 1/2 ft by 6 1/2 ft
C) 3 ft by 7 ft
D) 3 1/2 ft by 7 1/2 ft
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x = width

Since the "height is 4 feet more than its width", this means that the height is feet.

Start with Pythagoreans Theorem. Note: "a" and "b" are the legs of the triangle (in this case the width and height of the door) and "c" is the hypotenuse (which in this problem is the diagonal of the door)

Plug in (this is the width), (this is the height), and (which is given as the diagonal)

Square to get

Reduce

FOIL

Combine like terms.

Multiply every term by the LCD 2 to clear the fraction

Subtract 97 from both sides.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible widths are or (which in decimal form are or respectively)

However, since a negative width doesn't make sense, this means that the only solution is (which is the mixed fraction )

So the width is 2 and a half feet

Go back to the expression that represents the height

Plug in )

Add

So the height of the door is 6 and a half feet.

-------------------------------------
Answer:
So the dimensions of the door are feet by which means that the answer is B) 2 1/2 ft by 6 1/2 ft
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