NMTC Practice Part 6
Two sides of a triangle are 1 0 and 5 units in length, and the length of the median to the third side is 6 . 5 units. The area of the triangle is 6 x units squared. Determine the value of x .
This question has appeared in NMTC.
The answer is 14.
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3 solutions
same way!!!
I derived a formula for median and then used that formula to solve.
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Yes, the formula for median can be derived by stewart's theorem
Median of any triangle
=
2
1
2
A
B
2
+
2
A
C
2
−
B
C
2
Let median be
A
M
.
⇒
A
M
=
2
1
2
A
B
2
+
2
A
C
2
−
B
C
2
⇒
1
3
=
2
A
B
2
+
2
A
C
2
−
B
C
2
⇒
B
C
=
9
Now, by Heron's formula.
⇒
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
s
=
2
1
0
+
5
+
9
=
2
4
⇒
1
2
×
2
×
7
×
3
⇒
6
1
4
=
6
x
∴
x
=
1
4
Basically we just simply need to use Apollonius theorem and then use Heron's Formula for the area, I solved it using this method
Appollonius ,then use herons you will get the answer
By using Apollonius Theorem we get the half the third side 4.5,then the side is 9,By using Heron's law we get area 6 * sqrt 14.So x=14