Given:
In a right angle triangle ABC, altitude BD drawn to hypotenuse AC.
AD=3 and, AC=27.
To find:
The length of AB.
Solution:
Draw a figure by using the given information as shown below.
In triangle ABC and ADB,
[tex]\angle ABC\cong \angle ADB[/tex] (Right angles)
[tex]\angle BAC\cong \angle DAB[/tex] (Common angle)
[tex]\triangle ABC\sim \triangle ADB[/tex] (AA similarity postulate)
We know that the corresponding parts of congruent triangles are proportional. So,
[tex]\dfrac{AC}{AB}=\dfrac{AB}{AD}[/tex]
After substituting the given values, we get
[tex]\dfrac{27}{AB}=\dfrac{AB}{3}[/tex]
[tex]27\times 3=AB\times AB[/tex]
[tex]81=AB^2[/tex]
Taking square root on both sides, we get
[tex]\sqrt{81}=AB[/tex]
[tex]9=AB[/tex]
Therefore, the length of AB is 9 units.
