Question

Triangle ABC

is similar to
triangle DEF
. The length of
AC
¯
¯
¯
¯
¯
is 12 cm. The length of
BC
¯
¯
¯
¯
¯
is 18 cm. The length of
DF
¯
¯
¯
¯
¯
is 10 cm.

What is the length of
EF
¯
¯
¯
¯
¯
?

Answer 1

15 cm

Explanation:

Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.

A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

`(BC)/(EF) =(AC)/(DF)`.

`(18)/(x)=(12)/(10)`

To solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

`(18)/(x)=(12)/(10)\\ 18*10 = x*12 \\ 180 = 12x \\ 15 = x`