Find the value of x and please explain the answer
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SOLUTION
Let BC = 2y cm
By Apollonius's Theorem
So the sides are 5 cm, 10cm, 9 cm
∴ Area
=
Hence
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Answer:
SOLUTION
Let BC = 2y cm
By Apollonius's Theorem
{5}^{2} + {10}^{2} = 2 \times ( {6.5}^{2} + {y}^{2} )5
2
+10
2
=2×(6.5
2
+y
2
)
\implies \: 25 + 100 = 2( 42.25 + {y}^{2} )⟹25+100=2(42.25+y
2
)
\implies \: 2 {y}^{2} = 125 - 84.5⟹2y
2
=125−84.5
\implies \: {y}^{2} = 20.25⟹y
2
=20.25
\implies \: y \: = 4.5⟹y=4.5
So the sides are 5 cm, 10cm, 9 cm
s \: = \frac{(5 + 10 + 9)}{2} = 12s=
2
(5+10+9)
=12
∴ Area
= \sqrt{s(s - a \: )(s - b)(s - c)}
s(s−a)(s−b)(s−c)
= \sqrt{12 \times (12 - 4) \times (12 - 10) \times (12 - 9)} =
12×(12−4)×(12−10)×(12−9)
= \sqrt{12 \times 7 \times 2 \times 3} =
12×7×2×3
= 6\sqrt{14} =6
14
Hence
6 \sqrt{x} = 6\sqrt{14}6
x
=6
14
\implies \: \sqrt{x} =\sqrt{14} ⟹
x
=
14
\therefore \: \: x \: = 14∴x=14