Answer:
Length of hypotensue
=
3
√
10
Let the length of shorter side =
x
and length of longer side =
y
According to pythagoras theorem,
x
2
+
y
2
=
(
3
√
10
)
2
=
90
x
2
+
y
2
=
90
.
.
.
.
.
.
(
1
)
The smaller side is tripled
=
3
x
The larger side is doubled
=
2
y
New hypotenuse
=
9
√
5
Now,
(
3
x
)
2
+
(
2
y
)
2
=
(
9
√
5
)
2
9
x
2
+
4
y
2
=
405
5
x
2
+
4
x
2
+
4
y
2
=
405
5
x
2
+
4
(
x
2
+
y
2
)
=
405
5
x
2
+
4
×
90
=
405
5
x
2
=
405
−
360
x
2
=
45
5
x
2
=
9
x
=
3
Put
x
=
3
in (1) and we get,
y
=
9