Find the value of BE, if AB = 12 cm and BC = 9 cm and AE : EC = 3: 2.a)andradic;6 cmb)3andradic;6 cmc)andradic;12 cmd)2andradic;3 cmCorrect answer is option 'B'. Can you explain this answer?

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Find the value of BE, if AB = 12 cm and BC = 9 cm and AE : EC = 3 : 2.

a)
√6 cm
b)
3√6 cm
c)
√12 cm
d)
2√3 cm

Correct answer is option 'B'. Can you explain this answer?

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Find the value of BE, if AB = 12 cm and BC = 9 cm and AE : EC = 3: 2.a...

Given,
The Triangles on each side of altitude drawn from vertex of right angle to hypotenuse are similar to original triangle.

In ΔABC,
⇒ AC² = AB² + BC²
⇒ AC² = 12² + 9² = 225
⇒ AC = 15cm

Given,
⇒ AE : EC = 3 : 2
⇒ AE/(AC – AE) = 3/2
⇒ 2AE = 3AC – 3AE
⇒ 5AE = 3AC
⇒ AE = 3(15)/5
⇒ AE = 9 cm
⇒ EC = 15 – 9 = 6cm

The altitude from the vertex of the right angle triangle to the hypotenuse is the geometric mean of segments into which the hypotenuse is divided.

Then,
⇒ BE² = AE × EC
⇒ BE² = 6 × 9
⇒ BE = 3√6 cm

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