BD and CE are the medians of Δ ABC, right angled at A. If CE = 5√(13) over 2 cm, BC = 10 cm, then the length of BD is:

BD and CE are the medians of Δ ABC, right angled at A. If…

BD and CE are the medians of Δ ABC, right angled at A. If CE = ${5\sqrt{13} \over 2}$ cm, BC = 10 cm, then the length of BD is:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. $(5/2)\sqrt{7} cm$

CE = ${5\sqrt{13} \over 2}$ , BC = 10

AC² + AB² = BC²

We know that

BD²+ CE² =5/4(AB² + AC²)

BD² + ( ${5\sqrt{13} \over 2}$ )² = 5/4(BC²)

BD² + 325/4 = 5/4(100)

BD² = 500/4 - 325/4 = 175/4

BD = $(5/2)\sqrt{7} cm$