Question

Given right triangle ABC= with altitude BD drawn to hypotenuse AC. If AD=3 and, AC=27, what is the length of AB?

Answer 1

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,

$\angle ABC\cong \angle ADB$              (Right angles)

$\angle BAC\cong \angle DAB$              (Common angle)

$\triangle ABC\sim \triangle ADB$              (AA similarity postulate)

We know that the corresponding parts of congruent triangles are proportional. So,

$\dfrac{AC}{AB}=\dfrac{AB}{AD}$

After substituting the given values, we get

$\dfrac{27}{AB}=\dfrac{AB}{3}$

$27\times 3=AB\times AB$

$81=AB^2$

Taking square root on both sides, we get

$\sqrt{81}=AB$

$9=AB$

Therefore, the length of AB is 9 units.