Question

The value of Y is? I’ve been stuck on this for a while please help!

Answer 1

`14`

1) In this question, the initial step to tackle this is to consider that there are two triangles with parallel bases.

So, there are corresponding angles, therefore congruent. And we can infer that these triangles are similar.

2) Based on that, it is safe to say that the sides of the largest and the smallest triangle are proportional. So we can write out ratios and then find "y":

`\begin{gathered} (AB)/(AD)=(AC)/(AE) \\ (10)/(25)=(y)/(21+y) \\ 25y=10(21+y) \\ 25y=210+10y \\ 25y-10y=210 \\ 15y=210 \\ (15y)/(15)=(210)/(15) \\ y=14 \end{gathered}`

3) Thus, the answer is:

`14`