The hypotenuse of a right triangle is 15 centimeters long. One leg is 9 cm long. How do you find the length of the other leg?

2 Answers
Meave60
Mar 22, 2018

The other leg is #"12 cm"# long.

Explanation:

Use the Pythagorean theorem:

#c^2=a^2+b^2#,

where:

#c# is the hypotenuse, and #a# and #b# are the other two sides (legs).

Let #a="9 cm"#

Rearrange the equation to isolate #b^2#. Plug in the values for #a# and #c#, and solve.

#b^2=c^2-a^2#

#b^2=("15 cm")^2-("9 cm")^2#

Simplify.

#b^2="225 cm"^2-81 "cm"^2"#

#b^2="144 cm"^2"#

Take the square root of both sides.

#b=sqrt("144 cm"^2")#

Simplify.

#b="12 cm"#

CountryGirl
Mar 22, 2018

#12# centimeters long.

Explanation:

Since this is a right triangle, we can use the Pythagorean Theorem.

https://www.onlinemathlearning.com/pythagorean-theorem.html
#"c = hypotenuse"#
#"a = leg"#
#"b = leg"#

We can substitute in #c# (the hypotenuse) and #a# (one of the legs) to find the length of #b# (the other leg)
#a^2 + b^2 = c^2#
#9^2 + b^2 = 15^2#
#81 + b^2 = 225#
#b^2 = 144#
#b = sqrt144#
#b = 12#

So the other leg is #12# centimeters long.

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