Question

In the figure, AD is drawn perpendicular to the side opposite to the right angled vertex A. BC = 13 cm and AD = 6 cm.

a. Take BD = x and express DC in terms of x.

b. Frame a second-degree equation and find the lengths BD and DC.

Answer 1

a. let BD = x, DC = 13 - x

b. BC x DC = AD²

x(13 - x) = 6² 

13x - x² = 36

x² - 13x + 36 = 0

\(x=\frac{13\pm \sqrt{(-13)^2-4\times1\times36}}{2\times1}\)

∴ \(\frac{13\pm \sqrt{169-144}}{2}=\frac{13\pm \sqrt{25}}{2}\) = \(\frac{13\pm 5}{2}\)

BC = 9 centimetre, DC = 4 centimetre