Abc similar to def the area of abc is 45cm and the area of triangle def is 20cm one side of triangle abc is 3.6cm the the length of corresponding side of triangle def is

2.4cm

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

that means two lengths of the triangle have to be multiplied.

and to have 2 similar triangles means that all lengths inside one triangle are the corresponding lengths inside the other triangle multiplied by the scaling factor f.

multiplying 2 if these lengths with each other means also including the square of the scaling factor (multiplying with the scaling factor twice).

so, if the area of triangle 1 is

"baseline 1" × "height 1" / 2 = 45 cm²

then the area of triangle 2 is

"baseline 2" × "height 2" / 2 =

= "baseline 1"×f × "height 1"×f /2 =

= "baseline 1" × "height 1" × f² / 2 =

= ("baseline 1" × "height 1" / 2) × f² =

= 45 × f² = 20 cm²

f² = 20/45 = 4/9

f = 2/3

so, for a side of ABC being 3.6cm long, that means the corresponding side in DEF is

3.6 × f = 3.6 × 2/3 = 7.2/3 = 2.4cm

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

its 50 miles away from the starting point