Question

What is the length of CD? In this diagram, AABC~ AEDC.

Answer 1

The length of CD will be 3

From given diagram, triangle ABC and EDC meet at a common vertex C.

So, triangle ABC and EDC both are congruent to each other.

Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.

Therefore,

$\frac{AB}{ED} = \frac{AC}{EC} = \frac{BC}{CD}$

$\frac{AC}{EC} = \frac{BC}{CD}$

$\frac{18}{6} = \frac{12 - x}{x}$

Simplifying the expression,

We get

$18x = 6(12 - x)$

Multiplicating the terms in right hand side,

$18x = 72 - 6x$

Solving 6x on both sides,

we get

$18x + 6x = 72 - 6x + 6x$

$24x = 72$

Dividing both the sides by 24, we get

$\frac{24x}{24} = \frac{72}{24}$

$x = 3$

Hence, the length of CD is 3.

Learn more about congruent triangle here:

brainly.com/question/2938476

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