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Byju's Answer
Standard VII
Mathematics
Area of a Triangle
The area of a...
Question
The area of a right angled triangle is
40
sq.cm and its perimeter is
40
cm.Find the length of its hypotenuse.
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Solution
Let the hypotenuse
A
C
=
h
and the other two sides be
A
B
=
a
and
B
C
=
b
By Pythagoras theorem, we have
h
2
=
a
2
+
b
2
.....
(
1
)
Given:Area of
△
A
B
C
=
40
sq.m
Hence,
1
2
×
a
×
b
=
40
⇒
a
b
=
80
.......
(
2
)
Given perimeter of
△
A
B
C
=
40
cm
That is
a
+
b
+
h
=
40
⇒
a
+
b
=
40
–
h
Squaring on both the sides, we get
(
a
+
b
)
2
=
(
40
−
h
)
2
⇒
a
2
+
b
2
+
2
a
b
=
1600
−
80
h
+
h
2
⇒
h
2
+
2
(
80
)
=
1600
−
80
h
+
h
2
from
(
1
)
and
(
2
)
⇒
160
=
1600
−
80
h
⇒
80
h
=
1600
–
160
=
1440
∴
h
=
18
cm
Thus the length of hypotenuse is
18
cm.
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