Question

Triangle ABC

A
B
C
and triangle DEF
D
E
F
are similar. What is the measure of side DF
D
F
?

Answer 1

12

Explanation:

1. Use the Pythagorean theorem for triangle ABC

a squared (one side of the triangle) + b squared (another side) = c squared (hypotenuse)

so

c squared - b squared = a squared

225 - 81 = 144 ( Find the square root )

which is 12

since Triangle ABC is the same with Triangle DEF then

DF = 12

Answer 2

DF = 15 cm

Explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

`(DF)/(AC)` =
`(EF)/(BC)` ( substitute values )

`(DF)/(9)` =
`(25)/(15)` ( cross- multiply )

15 DF = 9 × 25 = 225 ( divide both sides by 15 )

DF = 15