The diagram shows triangle ABC with D on AC and E on AB. DE is a straight line. AD = 27 m, AE = 39 m, DE = 23m and BC = 65 m. Calculate the length CD.

Similar triangles may or may not be congruent

The length of CD is 49 units.

From the given triangles, we have the following equivalent ratios

Where:

So, we have:

Substitute known values

Express as fraction

Multiply both sides by 65

Subtract 27 from both sides

Rewrite as:

Hence, the length of CD is 49 units.

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CD is approximately 77.55 m

Step-by-step explanation:

I would start by finding the measure of <A using law of cosines

a²=b²+c²-2bc cos A

23²=27²+39²-2(27)(39) cos A

-1721 = -2106 cos A

A =

A = 35.2°

Then I would use law of sines

x/sin 68 = 65/sin 35.2,     x is the length of AC

x = 104.55, then subtract 27 to get the length of CD

CD is approximately 77.55 m

1/5x+9 2/5y+7

step-by-step explanation:

e) none of the above because the measure of angle cba is 101°