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mixas84 [53]
3 years ago
15

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

Mathematics
1 answer:
Kazeer [188]3 years ago
8 0

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.

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Hello, I can help you with this

to solve need  we will need these two equations

Step one

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I hope it helps,have a great day.

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