Practicing Success
In ΔABC, ∠B = 90°, AB = 8 cm and BC = 15 cm. D is a point on BC such that AD bisects ∠A. The length (in cm) of BD is : |
4.5 4.8 4.2 3.6 |
4.8 |
As , AD is bisector of angle ∠A. So, \(\frac{BD}{DC}\) = \(\frac{AB}{AC}\) By using pythagoras theorem , ( Hypotenuse )² = ( Perpendicular )² + ( Base )² ( AC )² = ( AB )² + ( BC )² ( AC )² = ( 8 )² + ( 15 )² ( AC )² = 64 + 225 = 289 AC = 17 Using , \(\frac{BD}{DC}\) = \(\frac{AB}{AC}\) \(\frac{BD}{DC}\) = \(\frac{8}{17}\) So, BD and DC id divided in ratio 8 : 17 According to question, 8R + 17R = 15 25R = 15 1R = \(\frac{3}{5}\) Now, BD = 8R = 8 x \(\frac{3}{5}\) = 4.8 cm
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