Your problem tells you that the height (H) of rectangular screen door is 4 feet more than

its width (W). In equation form this becomes:

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The problem also tells you that the diagonal (D) of this rectangular door is:

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and (calculator time) the square root of 194 is 13.92838828. Divide this by 2 and you

find that the diagonal of the door (in feet) is:

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Now you can apply the Pythagorean theorem which says that for a right triangle (formed

by the height, the width, and the diagonal of the door), the sum of the squares of each

of the legs of the triangle equals the square of the diagonal. For this problem you can

write the equation that:

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But from your first steps on this problem you know that H = W + 4, so you can substitute

W + 4 for H and the equation becomes:

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Square the (W + 4) term on the left and the equation becomes:

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Combine the two terms on the left side and the equation becomes:

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Next recall that earlier you found that the diagonal D was 6.964194139 feet. Square this

and you get that:

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In the quadratic equation substitute 48.5 for and the equation becomes:

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Get this into standard quadratic form by subtracting 48.5 from both sides. The result is:

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Although you do not need to do this next step, you can make the problem a little easier

by dividing both sides by 2 just to eliminate the 2 that multiplies the term.

When you do that division the quadratic equation becomes:

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Now you can apply the quadratic formula to solve this equation. The quadratic formula

says that for a quadratic equation of the form:

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the two solutions will be:

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By comparing your equation with the standard form you see that the corresponding factors

are: x = W, a = +1, b = +4, and c = -16.25

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Substitute these values into the solution equation and you get:

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This simplifies to:

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The term in the radical is 81 and its square root is 9. This simplifies your equation

to:

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This means your possible solutions are:

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and

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You can ignore the first solution because it is negative and having a negative width

for a screen door doesn't make sense. The second solution means that the width of the

door is 2.5 feet (or 30 inches). A little narrow by today's standard construction

but a reasonable answer. The height is 4 feet more than that (from your work at the

start of the problem) and that means the door is 2.5 + 4 = 6.5 feet (78 inches) tall.

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