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Byju's Answer
Standard IX
Mathematics
Area of an Equilateral Triangle
The differenc...
Question
The difference between the semi-perimeter and the sides of a
∆ABC are 8 cm, 7 cm and 5 cm respectively. The area of the triangle is
(a)
20
7
cm
2
(b)
10
14
cm
2
(c)
20
14
cm
2
(d) 140 cm
2
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Solution
(c)
20
14
cm
2
Let the sides of the triangle be a cm, b cm and c cm and the semi-perimeter be s cm.
Given:
s
-
a
=
8
cm
,
s
-
b
=
7
cm
and
s
-
c
=
5
cm
By adding all these, we get:
s
-
a
+
s
-
b
+
s
-
c
=
8
+
7
+
5
⇒
3
s
-
(
a
+
b
+
c
)
=
20
2
s
=
a
+
b
+
c
⇒
3
s
-
2
s
=
20
⇒
s
=
20
cm
By
applying
Heron
'
s
formula
,
we
get
:
Area
of
triangle
=
s
(
s
-
a
)
(
s
-
b
)
(
s
-
c
)
=
20
×
8
×
7
×
5
=
5
×
4
×
7
×
5
×
4
×
2
=
5
×
4
×
14
=
20
14
cm
2
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Similar questions
Q.
If the sides of a triangle are 3 cm, 4 cm and 5 cm respectively, then its area is 60
c
m
2
.
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