Question

In a triangle ABC, right-angled at B, AB=2cm. A point D lies on BC such that BD=1cm and AD=BC. Find AC.

Answer 1

$\textbf{\huge{ANSWER:}}$

Given:

Angle B = 90°

AB = 2 cm

BD = 1 cm

AD = BC

In Triangle ABD:
${AB}^{2} + {BD}^{2} = {AD}^{2}$ ( Due to the Pythagoras Theorem )

=》 ${2}^{2} + {1}^{2} = {AD}^{2}$

=》 $AD = \sqrt{5}$

BC = AD
Thus,
BC = Root 5

In Triangle ABC:
${AB}^{2} + {\sqrt{5}}^{2} = {AC}^{2}$

=》 $4 + 5 = {AC}^{2}$

=》 $\sqrt{9} = AC$

=》 $\textbf{AC = 3 cm}$

Hope it Helps!! :)