It is nonequivalent. Figure it out this way. Think about what number has to be multiplied by both the numerator and the denominator of to get to
. It has to be the samee number for the one expression to be equivalent to the other. To get from 5x to x^3, we have to multiply by 1/5x^2. When we do that we get x^3. Good. Now we have to multiply the denominator by the same thing, 1/5x^2.
. As you can see, they are not equivalent.
BO is double that of DO. In other words, BO is two times longer than DO. The answer is choice B
For example, if DO were 3 units long, then BO would be 6 units long (2*3 = 6). This works because the triangles DCO and BAO are similar triangles. The corresponding sides are in the same ratio or proportion to one another. The larger triangle (BAO) has sides that are twice as long as the smaller triangle's (DCO) corresponding sides.
Side note: we can prove the triangles to be similar using the AA (angle angle) similarity theorem. The first pair of angles are the vertical angles DOC and BOA which are congruent to each other.The second pair is CDB and ABD which are congruent by the alternate interior angle theorem. Check out the attached image for a visual.
