Question

HELP ME PLEASE ASAP SAT

Answer 1

It is written that the two triangles are similar. This means that we are to apply the method used for finding the missing lengths of similar triangles. The ratio of the side length and the width ΔDBE can be written as $\frac{4}{BE}$. A similar ratio can be set up for ΔABC. However, it is 6 units wide and the side length is 2 units longer, so our proportion will look like this: $\frac{6}{BE + 2}$. Now that we have both proportions, the only thing left to do is cross multiply to find the measure of $BE$. Try to think of BE as one variable instead of two. Multiply as shown:

$\frac{4}{BE} = \frac{6}{BE + 2}$

Cross multiply. --> $4(BE + 2) = 6(BE)$

Distribute. ---> $4BE + 8 = 6BE$

Isolate variable BE. ----> $4BE + 8 - 6BE - 8 = 6BE - 6BE - 8$

-2BE = -8

But there is no such thing as negative measurements, so simply flip the equation like this:

$2BE = 8$

Once more isolate the variable. --> $\frac{2BE}{2} = \frac{8}{2}$

---> $BE = 4$

Your answer is C.

Answer 2

The answer is 4

4/x=6/x+2

⇒x=4

Not that hard :VV