Maths-
General
Easy

Question

# Triangles  ABC and DEF  above are similar. How much longer than segment EF  is segment  DE ?

Hint:

## The correct answer is: 2

### Given,∆ABC and ∆DEF are similar.By the property of similar triangles, we now that the corresponding sides have the same ratio, that is,∆ABC and ∆DEF are similar.By the property of similar triangles, we now that the corresponding sides have the same ratio, that is,We are also given that,Inputting these values in the expression above, we getSimplifying it, we haveFrom the first and the third values, we get,Thus, the value of DE is given bySimilarly, from the second fraction, we have,Thus, the value of EF is given byNow,Thus, DE is longer than EF by 2The correct option is B)

Note:
There are three ways to prove that two triangles are similar- AAA,
SAS, SSS.
AAA means that the corresponding angles are equal,
SAS means two sides of the triangles are in equal ratio and the angles between these two sides are equal,
SSS means that all three corresponding sides have equal ratio