Question

the sides of a right triangle are 9,12and 15 cm long. then the sum of the square of median is(in cm)..
a)300
b)400
c)337.5
d)250.5​

Answer 1

Option (c) is the correct option ✔️✔️

Answer:

• The sum of the square of median is = 337.5 cm.

Given :

• Sides, AB = 9 cm , BC = 12 cm, CA = 15 cm

To find :

• The sum of the square of median is =?

Step-by-step explanation:

Using Apollonius Theorem :

3(AB² + BC² + AC²) = 4 (AD² + BE² + CF²)

AB = 9 cm , BC = 12 cm, CA = 15 cm

AD, BE, CF are median,

AD² + BE² + CF² = 3/4(AB² + BC² + AC²)

Substituting the values, we get,

= 3/4 [(9²) + (12²) + (15²)]

= 3/4 [ 81 + 144 + 225 ]

= 3/4 x 450

= 337.5 cm.

Hence,

The sum of the square of median is = 337.5 cm.

Answer 2

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