Find the hypotenuse of the right isosceles triangle each of whose
legs is l.
Answers
Answer:
How do you find the length of each leg of an isosceles right triangle whose hypotenuse is 14 cm?
Geometry
1 Answer
CW
Mar 4, 2017
14
√
2
=
7
√
2
Explanation:
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An isosceles right triangle is a right triangle with two legs equal in length and has angles of
45
∘
−
45
∘
−
90
∘
.
By Pythagorean Theorem, we know that,
hypotenuse
c
2
=
a
2
+
a
2
,
⇒
c
=
a
√
2
where
c
is the hypotenuse and
a
is the leg.
So for an isosceles right triangle with side length
a
, the hypotenuse has a length of
a
√
2
.
Similarly, if the hypotenuse of an isosceles right triangle has length of
a
, the legs have a length of
a
√
2
or
a
√
2
2
each.
Given that the hypotenuse of the isosceles right triangle
=
14
,
⇒
the length of each leg
=
14
√
2
=
7
√
2
Check :
(
7
√
2
)
2
+
(
7
√
2
)
2
=
196
=
14
2
(OK)