Question

Can someone help me?

Answer 1

Answer:

Step-by-step explanation:

To start calculating, we first need to make some proof.

Firstly, since AB = AC, we know that ΔABC is isosceles, which means that ∠ABC = ∠ACB.

Now, looking only to ΔBDE and ΔCDF, we can see that they are similar, because the two of its angles are congruent:

∠BED=∠CFD

∠DBE=∠DCF

To make it easier to visualize which are the corresponding vertexes, we can draw them like this:

And we need to remember that BC is 24, so:

BD+CD=24

Since the triangles are similar, their corresponding sides have constant ratio, which we can calculate from the corresponding sides DE and CF:

$r=\frac{CF}{DE} =\frac{7.5}{4.5} =\frac{5}{3}$

This ratio is the same for the other corresponding sides, so we can apply that for BD and CD:

$r=\frac{CD}{BD} =\frac{5}{3}\\ \frac{BD}{CD}=\frac{3}{5} \\\\ BD=\frac{3}{5} Cd$

Thus, the measure of CF is approximately 13, alternative D.