Pythagorean Theorem Practice
Problems
More Challenging!
Problem 1
Solve for the missing side
of the triangle.
Solution
The missing side has length
~6.08.
Using the Pythagorean
Theorem, a2+b2=c2. The
missing side, since it’s the
hypotenuse, has length c.
Plugging in known values:
20 + 17 = c2.
Simplify.
c2 = 37
Take the square root of both
sides of the equation.
c ≈ 6.08
Problem 2
Bob has a 15 foot long
ladder. The instructions
for the ladder tell him
that he should put the
base at least 8 feet
away from the base of
whatever he’s using the
ladder to climb. How
tall is the tallest building
that Bob can scale using
his ladder?
Image source:
http://www.inkity.com/shirtdesigner/prints
/clipArt1/S7531210.png
Solution
Bob will be able to reach the
maximum possible height
when the ladder is as
close to the building as
possible. Thus, the height
will be one leg of a right
triangle with hypotenuse
15 and base 8. Using the
Pythagorean Theorem:
H2 + 82=152
H2 = 161
H ≈ 12.69
Problem 3
What is the length of the
hypotenuse of this
triangle with legs of
length 3x – 2 and 2x + 2
and with hypotenuse of
length 3x + 3?
Solution
The hypotenuse has a length of roughly 19.62.
Steps:
Begin by forming a relationship between the
three sides using the pythagorean
theorem.
(3x-2)2 + (2x+2)2 = (3x+3)2
Simplify by expanding and combining like
terms.
4x2 – 22x – 1 = 0
Solve for x using the Quadratic Formula.
Disregarding the negative result, we see that x
is equal to about 5.54, so we can solve for
the lengths of the sides by plugging them
into the original equations.