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A right triangle has a hypotenuse of 15 cm. What is the length for the missing leg if one of the two legs of the triangle is 5?
Question
A right triangle has a hypotenuse of 15 cm. What is the length for the missing leg if one of the two legs of the triangle is 5?
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Mathematics
4 years
2021-08-24T16:08:17+00:00
2021-08-24T16:08:17+00:00 2 Answers
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Answers ( )
Answer:
The other leg is 12 cm long.
Step-by-step explanation:
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
=
√
144 cm
2
Simplify.
b
=
12 cm
Answer:
14.14 cm
Step-by-step explanation:
using the Pythagorean theorem:
?² = 15² – 5² = 225 – 25 = 200
? = √200 = 14.14 cm