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seropon [69]
2 years ago
11

The perimeter of a triangle is 84 meters. The longest side of the triangle is 7 meters less than twice the length of the shortes

t side ,x. The middle side is 7 meters longer than the shortest side. What is the length of each side of the triangle.
Mathematics
1 answer:
vlada-n [284]2 years ago
6 0

Hey ! there

Answer:

  • Smallest side = <u>2</u><u>1</u><u> </u><u>m</u>

  • Middle side = <u>2</u><u>8</u><u> </u><u>m</u>

  • Longest side = <u>35</u><u> </u><u>m</u>

Step-by-step explanation:

In this question we are given that <u>perimeter</u> <u>of a triangle is </u><u>8</u><u>4</u><u> </u>m , <u>longest</u><u> </u><u>side </u><u>of </u><u>triangle </u><u>is </u><u>7</u><u> </u><u>meters</u><u> </u><u>less </u><u>than </u><u>twice </u><u>the </u><u>length </u><u>of </u><u>shortest </u><u>side </u><u>that </u><u>is </u><u>x </u><u>and </u><u>middle </u><u>side </u><u>is </u><u>7</u><u> </u><u>meters</u><u> </u><u>longer </u><u>than</u><u> </u><u>the </u><u>shorte</u><u>st </u><u>side </u><u>.</u>

And we're asked to find the <u>length</u><u> of</u><u> </u><u>each </u><u>side </u><u>o</u><u>f </u><u>triangle</u><u>. </u>

<u>So </u><u>,</u>

  • Shortest side = <u>x m </u>

  • Middle side = <u>( x + 7 ) </u>m ( Because in question it is given that middle side is 7 metres longer than the shorter side )

  • Longest side =<u> ( 2x -7 ) m</u> ( Because in question it is given that longest side is 7 m less than twice the length of shortest side )

<u>We </u><u>know</u><u> that</u><u> </u><u>,</u>

<u>\underline{\boxed{\frak{Perimeter_{(Triangle)} = Sum \:of\: three\: sides}}}</u>

<u>Solution</u><u> </u><u>:</u><u> </u><u>-</u>

\longmapsto \qquad x +( x + 7) + (2x - 7) = 84

<u>Step </u><u>1</u><u> </u><u>:</u> Removing parenthesis and cancelling 7 with -7 :

\longmapsto \qquad x + x + \cancel{7} +  2x - \cancel{ 7 }= 84

<u>Step </u><u>2</u><u> </u><u>:</u> Adding like terms on left side :

\longmapsto \qquad 4x = 84

<u>Step </u><u>3 </u><u>:</u> Dividing with 4 on both sides :

\longmapsto \qquad \dfrac{ \cancel{4}x}{ \cancel{4}}  =   \cancel{\dfrac{ 84}{4} }

On calculating further, We get :

\longmapsto \qquad \red{\underline{\boxed{\frak{ x = 21 \: m}}}}\quad \bigstar

<u>According</u><u> to</u><u> question</u><u> </u><u>,</u>

  • x = smallest side

  • <u>Henceforth</u><u> </u><u>,</u><u> </u><u>smallest</u><u> </u><u>side </u><u>of </u><u>triangle </u><u>is </u><u>2</u><u>1</u><u> </u><u>meters </u><u>.</u>

<u>▬▬▬▬▬▬▬▬▬▬▬▬▬▬</u>

  • x + 7 = middle side
  • 21 + 7 = 28

  • <u>Henceforth</u><u> </u><u>,</u><u> </u><u>middle</u><u> side</u><u> of</u><u> triangle</u><u> is</u><u> </u><u>1</u><u>3</u><u> </u><u>meters </u><u>.</u>

<u>▬▬▬▬▬▬▬▬▬▬▬▬▬▬</u>

  • 2x - 7 = longest side
  • 2(21) - 7
  • 42 - 7
  • 35

  • <u>Henceforth</u><u> </u><u>,</u><u> </u><u>longest </u><u>side </u><u>of </u><u>triangle</u><u> </u><u>is </u><u>35</u><u> </u><u>met</u><u>e</u><u>r</u><u>s </u><u>.</u>

<u>Verifying</u><u> </u><u>:</u><u> </u><u>-</u>

Now we are checking our answer by adding all the sides and equating it with given perimeter that is 84 metres .

  • 21 + 28 + 35 = 84

  • 49 + 35 = 84

  • 84 = 84

  • L.H.S = R.H.S

  • Hence , Verified .

<u>Therefore</u><u> </u><u>,</u><u> </u><u>our </u><u>answer</u><u> is</u><u> correct</u><u>. </u>

<h2><u>#KeepLearning</u></h2>
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