Question

1. The sides of a triangle are 18 cm, 24 cm and 34 cm. Find the length of the median to the 24 cm side.

Answer 1

Answer: 24.4cm

Step-by-step explanation:

4(M)^2 = 2(18)^2 + 2(34)^2 - (24)^2

4(M)^2 = 2385

M^2 = 2385÷4

M^2 = 596

M = sqrt (596)

M = 24.413

Answer 2

Let,s consider ABC is a Δ,

where, AB = 18cm.

            BC= 24cm.

            CA= 34cm.

According the question , we have to find out the length of the median to the 24 cm side.

We draw AD on BC in the point D.

Hence AD will be the median to the 24 cm side.

Let,s calculate the length of median AD:-

Median AD :- [√$\frac{2AB^{2} }{4}$ + √$\frac{2AC^{2} }{4}$ ⁻ √ $\frac{BC^{2} }{4}$] cm

                    ⇒[√ ( $\frac{2AB^{2}+ 2 AC^{2} - BC^{2} }{4}$) ]cm

                    ⇒[√$\frac{2 ( 18)^{2} + 2 (34)^{2}- (24)^{2} }{4}$] cm

                    ⇒[√(648 + 2312 - 576)÷4] cm

                    ⇒(√$\frac{2384}{4}$ )cm

                    ⇒(√ 596)cm

                    ⇒ 24.41 cm

∴  The length of the median to the 24 cm side will be 24.41cm

Ans :-  The length of the median to the 24 cm side will be 24.41cm.

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