Question

in the fingure,the angle BAC is a right angle and a D is a perpendicular to BC a b is equal to 4 centimetre AC is equal to 3 cm and BD is equal to x calculate x

Answer 1

In triangle ABC,
${ab}^{2} + {ac}^{2} = {bc}^{2} \\ {4}^{2} + 3 ^{2} = {bc}^{2} \\ 5 = bc$
As BD=x, then CD=5-x

Applying pythagoras theorem in triangles BDC and CDA
${bd}^{2} + {ad}^{2} = {4}^{2} \\ {cd}^{2} + {ad}^{2} = {3}^{2}$
Eliminate AD^2 from the equations, you will get,
${4}^{2} - {bd}^{2} = {3}^{2} - {cd}^{2} \\ {4}^{2} - {x}^{2} = {3}^{2} - {(5 - x)}^{2} \\ x = \frac{16}{5} cm$