Question

AABC is similar to ADEF and AB = 5, BC= 8. If DE = 17.5

then which of the following would be the length of EF?
A
B
C
D
12.5
15
25
28

Answer 1

EF = 28.

Explanation:

If two triangles Δ ABC and Δ DEF are similar, then the ratio of the lengths of corresponding sides of Δ ABC and Δ DEF will be constant.

Therefore, we can write

`(AB)/(DE) = (BC)/(EF) = (CA)/(FD)` .............. (1)

Now, AB, BC, and DE are given to be 5, 8, and 17.5

And we have to find the length of EF.

So, from equation (1), we get

`(5)/(17.5) = (8)/(EF)`

⇒
`EF = 8 * (17.5)/(5) = 28`. (Answer)