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, a2+b2=c2
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
12 + b2 = 7.52, a quadratic equation
in b.
Applying the addition property of equality and subtracting 12
from both sides results in b2 = 7.52 - 12
or b2 = 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.
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