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Sagot :

Starrysoul100

[tex]\bold{\huge{\underline{ Solution \:1}}}[/tex]

Here, We have given

  • The sides of a triangle are 8 , 15 and 18
  • The one of the side of the similar traingle is 10.

Let assume the given triangle as ΔABC and ΔXYZ

According to the similarity theorem

  • If two triangle's are similar then the ratio of their corresponding sides are also equal .

Therefore, By using above theorem :-

[tex]\sf{\dfrac{ A}{X}}{\sf{=}}{\sf{\dfrac{ B}{Y}}}{\sf{=}}{\sf{\dfrac{ C}{Z}}}[/tex]

Subsitute the required values

[tex]\sf{\dfrac{ 8}{10}}{\sf{=}}{\sf{\dfrac{ 15 }{Y}}}{\sf{=}}{\sf{\dfrac{18}{Z}}}[/tex]

For other two sides of another similar triangle

[tex]\sf{\dfrac{ 8 }{10}}{\sf{=}}{\sf{\dfrac{ 15}{Y}}}[/tex]

[tex]\sf{Y =15}{\sf{\times{\dfrac{ 10}{8}}}}[/tex]

[tex]\sf{Y =15}{\sf{\times{\dfrac{ 5}{4}}}}[/tex]

[tex]\sf{Y = }{\sf{\dfrac{ 75}{4}}}[/tex]

[tex]\bold{Y = 18.75 }[/tex]

And,

[tex]\sf{\dfrac{ 8 }{10}}{\sf{=}}{\sf{\dfrac{ 18}{Z}}}[/tex]

[tex]\sf{Z =18 }{\sf{\times{\dfrac{ 10}{8}}}}[/tex]

[tex]\sf{Z =18}{\sf{\times{\dfrac{ 5}{4}}}}[/tex]

[tex]\sf{Z = }{\sf{\dfrac{ 90}{4}}}[/tex]

[tex]\bold{Z = 22.5 }[/tex]

Hence, The two sides of the another similar triangle is 18.75 and 22.5

[tex]\bold{\huge{\underline{ Solution \:2}}}[/tex]

Here, We have

  • Two similar triangles
  • Whose sides are 4 , 12 ,20 and 5 , 15 , 25

Let assume the two triangle be ΔABC and ΔPQR

According to the similarity theorem :-

  • If two triangle's are similar then the ratio of their corresponding sides are also equal .

That is,

[tex]\sf{\dfrac{ A}{P}}{\sf{=}}{\sf{\dfrac{ B}{Q}}}{\sf{=}}{\sf{\dfrac{ C}{R}}}[/tex]

Subsitute the required values,

[tex]\sf{\dfrac{4 }{5}}{\sf{=}}{\sf{\dfrac{ 12}{15}}}{\sf{=}}{\sf{\dfrac{ 20 }{25}}}[/tex]

[tex]\sf{\dfrac{4 }{5}}{\sf{=}}{\sf{\cancel{\dfrac{ 12}{15}}}}{\sf{=}}{\sf{\cancel{\dfrac{ 20 }{25}}}}[/tex]

[tex]\bold{\dfrac{4 }{5}}{\sf{=}}{\bold{\dfrac{ 4}{5}}}{\sf{=}}{\bold{\dfrac{ 4 }{5}}}[/tex]

Hence, The scale factor of the given similar triangles is 4/5

[tex]\bold{\huge{\underline{ Solution \: 3}}}[/tex]

Here, we have given that

  • A map in Davao City has a scale factor of 1 cm to 0.5 km
  • That is,
  • 1 : 0.5

But,

  • We have to find the distance corresponds to an actual distance of 12 km.

Therefore,

According to the scale factor

The actual distance will be

[tex]\sf{=}{\sf{\dfrac{ 12 }{0.5}}}[/tex]

[tex]\bold{ = 24 \: km }[/tex]

Hence, The map distance corresponds to actual distance of 12 km is 24 km.

#3 Answer:

The other sides are 18.75 and 22.5

#3 Step-by-step explanation:

Because of the similar triangle

So, [tex]\frac{8}{10}=\frac{15}{x}=\frac{18}{y}[/tex]               [tex]\left\{The\ corresponding\ sides\ are\ proportional\right\}[/tex]

[tex]x=18.75,\ y=22.5[/tex]

#4 Answer:

4:5

#4 Step-by-step explanation:

[tex]\frac{4}{5}=\frac{12}{15}=\frac{20}{25}=\frac{6}{5}[/tex]

[tex]So\ the\ scale\ factor\ is\ 4:5[/tex]

#5 Answer:

24 cm

#5 Step-by-step explanation:

[tex]12\div0.5[/tex]

Calculate

[tex]\frac{12}{0.5}[/tex]

Multiply both the numerator and denominator with the same integer

[tex]\frac{120}{5}[/tex]

Cross out the common factor

24

I hope this helps you

:)

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