plese refer above image
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after solving we get the value of x by similarity
hypotenuse=4√2×√2=8
so, perimeter=
1st option
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Answer:
Perimeter =
27
+
36
+
45
=
108
Explanation:
If
ˆ
Q
is
90
°
, then
P
R
is the hypotenuse.
P
Q
and
R
Q
can be written in terms of the hypotenuse.
Let
P
R
=
x
Then
P
Q
=
x
−
9
and
R
Q
=
x
−
18
Write an equation using Pythagoras' Theorem:
(
x
−
9
)
2
+
(
x
−
18
)
2
=
x
2
x
2
−
18
x
+
81
+
x
2
−
36
x
+
324
=
x
2
x
2
−
54
x
+
405
=
0
(
x
−
45
)
(
x
−
9
)
=
0
∴
x
=
45
or
x
=
9
→
reject
9
as being too short
If the hypotenuse is
45
, then the sides are
45
−
9
=
36
and
45
−
18
=
27
Perimeter =
27
+
36
+
45
=
108
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