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

Answer:

EF = 28.

Step-by-step 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

$\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}$ .............. (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

$\frac{5}{17.5} = \frac{8}{EF}$

⇒ $EF = 8 \times \frac{17.5}{5} = 28$. (Answer)