The lengths of the sides of a triangle in units ABC are AB-10- BC-7- CA-37 then length of the median through vertex C is

Length of median through nbsp; vertex C=12√(2 a^2+2 b^2 c^2) (Apollonius theorem) where a=BC=7, b=AC=√(3)7 , c=AB=10 Thus length of median=3√(2) units ...

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Standard XII

Mathematics

Solution of Triangle

The lengths o...

Question

The lengths of the sides of a triangle (in units) $A B C$ are $A B = 10, B C = 7, C A = \sqrt{37}$ then length of the median through vertex $C$ is

3 \sqrt{2}

units

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2 \sqrt{3}

units

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3 \sqrt{3}

units

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4 \sqrt{2}

units

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Solution

The correct option is A $3 \sqrt{2}$ units
Length of median through vertex $C = \frac{1}{2} \sqrt{2 a^{2} + 2 b^{2} - c^{2}}$ (Apollonius theorem)
where $a = B C = 7, b = A C = \sqrt{3} 7, c = A B = 10$
Thus length of median $= 3 \sqrt{2}$ units

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The lengths of the sides of a triangle (in units) ABC are AB=10,BC=7,CA=√37 then length of the median through vertex C is

The correct option is A 3√2 unitsLength of median through vertex C=12√2a2+2b2−c2 (Apollonius theorem) where a=BC=7,b=AC=√37,c=AB=10 Thus length of median=3√2 units

The lengths of the sides of a triangle (in units) $A B C$ are $A B = 10, B C = 7, C A = \sqrt{37}$ then length of the median through vertex $C$ is

The correct option is A $3 \sqrt{2}$ units
Length of median through vertex $C = \frac{1}{2} \sqrt{2 a^{2} + 2 b^{2} - c^{2}}$ (Apollonius theorem)
where $a = B C = 7, b = A C = \sqrt{3} 7, c = A B = 10$
Thus length of median $= 3 \sqrt{2}$ units