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Byju's Answer
Standard IX
Mathematics
Construction of Triangle 1
A right angle...
Question
A right angled triangle ABC is constructed with BC = 3
cm
and AB + AC = 9
cm
. If B is the right angled, then find the length of AC (in cm).
5
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Solution
The correct option is
A
5
The steps to construct the triangle is as follows.
Step 1: The segment BC is drawn.
Step 2: Construct
∠
C
B
X
=
90
∘
.
Step 3: An arc of radius 9 cm (AB+AC) is drawn from B on BX such that BD = 9 cm.
Step 4: The perpendicular bisector (MN) of CD is constructed which intersects BD at point A.
Step 5: A and C are joined.
△
A
B
C
is the required triangle.
In
△
A
B
C
, let the length of AC be
x
.
A
B
+
A
C
=
9
,
A
B
=
9
−
x
.
By using Pythogoras' theorem
A
B
2
+
B
C
2
=
A
C
2
.
∴
(
9
−
x
)
2
+
3
2
=
x
2
⇒
9
2
−
18
x
+
x
2
+
9
=
x
2
⇒
−
18
x
+
x
2
−
x
2
=
−
9
−
81
⇒
−
18
x
=
−
90
⇒
x
=
−
90
−
18
⇒
x
=
5
.
Thus, the length of AC is 5 cm.
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Q.
A right angled triangle ABC is constructed with BC = 3
cm
and AB + AC = 9
cm
. If B is the right angled, then find the length of AC (in cm).