If the perimeter of a triangle is 36 cm. Its inner radius is 4.5 cm. Is. Find its area.
Answers
Answered by
2
Answer:
Answer
Correct option is
B
54 cm
2
Given;-
perimeter=36
let the ratio be x
therefore,
⇒AB+BC+CA=36
⇒3x+4x+5x=36
⇒12x=36
⇒x=
12
36
⇒x=3
Now, putting the value of x
AB=3x=9cm
BC=4x=12cm
AC=5x=15cm
On using Pythagoras theorem
AC
2
=AB
2
+BC
2
=(9)
2
+(12)
2
=81+144
AC
2
=225
AC=15cm
ΔABC is right angled triangle ∠B is right angle.
Area of
ΔABC=
2
1
AB×BC
=
2
1
×9×12
=54cm
2
hence,
Area of triangle is 54cm
2
Answered by
1
Step-by-step explanation:
perimeter=36
let the ratio be x
therefore,
⇒AB+BC+CA=36
⇒3x+4x+5x=36
⇒12x=36
⇒x=
12
36
⇒x=3
Now, putting the value of x
AB=3x=9cm
BC=4x=12cm
AC=5x=15cm
On using Pythagoras theorem
AC
2
=AB
2
+BC
2
=(9)
2
+(12)
2
=81+144
AC
2
=225
AC=15cm
ΔABC is right angled triangle ∠B is right angle.
Area of
ΔABC=
2
1
AB×BC
=
2
1
×9×12
=54cm
2
hence,
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