Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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.

#KeepLearning

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.