Question

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Answer 1

We can use Pythagorean theorem.

We are given the medians. Let the halved length of AB and BC be x and y respectively.

From the length of AC,

→ AC²=(2x)²+(2y)²

→ 25=4x²+4y² ··· (A)

From the length of AD,

→ AD²=(2x)²+y²

→ 45/4=4x²+y² ··· (B)

From the length of CE,

→ CE²=x²+(2y)²

→ CE²=x²+4y² ··· (C)

EDIT: We can skip equation solving and find CE directly.

In this method, I will find the sum of (B)+(C).

(From B+C,) AD²+CE²=5x²+5y²

(From A,) AD²+CE²=125/4

(From B,) 45/4+CE²=125/4

→ CE²=60/4=15

Lengths are always positive. So, length CE is √15.