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Alchen [17]
3 years ago
5

What is the length of segment AE?

Mathematics
1 answer:
nexus9112 [7]3 years ago
6 0

Answer:

AE=\frac{50}{3}\ units

Step-by-step explanation:

step 1

In the right triangle ABC

Applying the Pythagoras Theorem fin the hypotenuse AC

AC^{2} =AB^{2}+BC^{2}

substitute

AC^{2} =6^{2}+8^{2}

AC^{2} =100

AC =10\ units

step 2

we know that

If two figures are similar, then the ratio of its corresponding sides is equal

so

\frac{AB}{CD}=\frac{AC}{CE}

substitute and solve for CE

\frac{6}{4}=\frac{10}{CE}\\ \\CE=4*10/6\\ \\CE=\frac{20}{3}\ units

step 3

Find the length of segment AE

AE=AC+CE

substitute the values

AE=10\ units+\frac{20}{3}\ units=\frac{50}{3}\ units

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