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

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,

             (Right angles)

             (Common angle)

             (AA similarity postulate)

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

After substituting the given values, we get

Taking square root on both sides, we get

Therefore, the length of AB is 9 units.

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b.-4 units

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