IDNLearn.com: Your one-stop platform for getting reliable answers to any question. Discover the information you need from our experienced professionals who provide accurate and reliable answers to all your questions.

please answer all questions ty :)

Please Answer All Questions Ty class=

Sagot :

Answer:

Scale factor: [tex]1.33333...=4/3[/tex]

Actual area: [tex]27[/tex]

Scale drawing area: [tex]48[/tex]

Ratio of areas: [tex]16/9[/tex]

Scale factor 2: [tex]4[/tex]

Scale factor [tex]1/3[/tex]: [tex]1/9[/tex]

Scale factor [tex]4/3[/tex]: [tex]16/9[/tex]

Observation: The ratio of the areas of the triangles is the square of the scale factor of the sides

Scale factor [tex]r[/tex]: [tex]r^2[/tex]

Step-by-step explanation:

The scale factor is [tex]12/9=8/6=4/3=1.333333...[/tex]

The actual area is [tex](6*9)/2=54/2=27[/tex]

The scale drawing area is [tex](12*8)/2=12*4=48[/tex]

Ratio of areas: [tex]48/27=16/9[/tex]

When the scale factor of the sides was 2, then the value of the ratio of the areas was 4.

When the scale factor of the sides was [tex]1/3[/tex], then the value of the ratio of the areas was [tex]1/9[/tex].

When the scale factor of the sides was [tex]4/3[/tex], then the value of the ratio of the areas was [tex]16/9[/tex].

Observation: The ratio of the areas of the triangles is the square of the scale factor of the sides.

If the scale factor is [tex]r[/tex], then the ratio of the areas is [tex]r^2[/tex], based on the observation.

Extra: Proof of observation.

Let the legs of the actual triangle be [tex]a[/tex] and [tex]b[/tex]. Then the legs of the scale triangle are [tex]ra[/tex] and [tex]rb[/tex], with [tex]r[/tex] being the scale factor.

The area of the actual triangle is [tex]ab/2[/tex]. The area of the scale triangle is [tex]ra*rb/2=r^2ab/2[/tex].

The ratio of these areas is [tex](r^2ab/2)/(ab/2)=r^2ab/ab=\boxed{r^2}[/tex], as desired.