A Simple But Common Application of Quadratic Equations
Introduction: Anyone that builds anything with a 90 degree angle
will sooner or later need to use the Pythagorean Theorem which states:
For any right triangle with sides of length a, b, and c, a^{2}+b^{2}=c^{2}
with c being the longest side or hypotenuse.
Example: I encountered a problem very similar to this when
building a roof on a greenhouse. The dimensions consist of a rafter
length c=7.5ft (so I can use 8ft lumber for my rafters) and height
a=1ft as shown below. What will be the width of the greenhouse
W?
Here, we need to let W/2 = b where "b" is the length of the
bottom side of the two equivalent right triangles. We get the equation
1^{2} + b^{2} = 7.5^{2}, a quadratic equation
in b.
Applying the addition property of equality and subtracting 1^{2}
from both sides results in b^{2} = 7.5^{2}  1^{2}
or b^{2} = 55.25 .
Extracting square roots from both sides results in b = 7.433 ft
(rounded). Since 2b = W, W=14.87 ft (rounded). We can
convert the 0.87ft into inches by multiplying 0.87ft by 12in/ft to get
10.44 inches (rounded). You can convert the 0.44 inches to 1/16ths of
an inch by multiplying 0.44 in by (16 sixteenths/1 in) to get 7/16.
So the total width is W= 14feet, 10 7/16 inches.
More Examples I Found
Waybuilder.net  Determine boundaries of building layout by
using the Pythagorean Theorem to calculate the diagonals.
Contractortalk.com  "I need help with this question on roof
framing."
Lowes.com  Finding squares on large projects.
Servicemagic.com  Framing rake walls.
