Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

hello help me with this question thanks in advance​

Hello Help Me With This Question Thanks In Advance class=

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

:)

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.