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The perimeter of a triangle is 84 meters. The longest side of the triangle is 7 meters less than twice the length of the shortest side ,x. The middle side is 7 meters longer than the shortest side. What is the length of each side of the triangle.

Sagot :

TheAmethyst

Hey ! there

Answer:

  • Smallest side = 21 m

  • Middle side = 28 m

  • Longest side = 35 m

Step-by-step explanation:

In this question we are given that perimeter of a triangle is 84 m , longest side of triangle is 7 meters less than twice the length of shortest side that is x and middle side is 7 meters longer than the shortest side .

And we're asked to find the length of each side of triangle.

So ,

  • Shortest side = x m

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

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

We know that ,

[tex]\underline{\boxed{\frak{Perimeter_{(Triangle)} = Sum \:of\: three\: sides}}}[/tex]

Solution : -

[tex] \longmapsto \qquad x +( x + 7) + (2x - 7) = 84[/tex]

Step 1 : Removing parenthesis and cancelling 7 with -7 :

[tex] \longmapsto \qquad x + x + \cancel{7} + 2x - \cancel{ 7 }= 84[/tex]

Step 2 : Adding like terms on left side :

[tex] \longmapsto \qquad 4x = 84[/tex]

Step 3 : Dividing with 4 on both sides :

[tex] \longmapsto \qquad \dfrac{ \cancel{4}x}{ \cancel{4}} = \cancel{\dfrac{ 84}{4} }[/tex]

On calculating further, We get :

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

According to question ,

  • x = smallest side

  • Henceforth , smallest side of triangle is 21 meters .

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

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

  • Henceforth , middle side of triangle is 13 meters .

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

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

  • Henceforth , longest side of triangle is 35 meters .

Verifying : -

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 .

Therefore , our answer is correct.

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