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Sagot :
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 .
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- 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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