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[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The longest side measures :

  • [tex]27\: \: cm[/tex]

[tex] \large \boxed{ \mathfrak{Explanation}}[/tex]

Perimeter of a triangle is equal to sum of measures of its all three sides, that is :

  • [tex]x + x + 8 + x + 12[/tex]

and according to the question, the perimeter of the triangle is = 65 cm

so, let's equate both the expressions to find value of x :

  • [tex]x + x + 8 + x + 12 = 65[/tex]
  • [tex]3x + 20 = 65[/tex]
  • [tex]3x = 65 - 20[/tex]
  • [tex]3x = 45[/tex]
  • [tex]x = 45 \div 3[/tex]
  • [tex]x = 15[/tex]

The longest side of the Triangle is :

  • [tex]x + 12[/tex]
  • [tex]15 + 12[/tex]
  • [tex]27 \: \: cm[/tex]

deeomoruyi75

27cm

Step-by-step explanation:

(xcm) + (x+8cm) + ( x+ 12cm) = 65cm

Open Bracket

xcm + x+8cm + x+12cm = 65cm

3x+ 20cm = 65cm

Collect like terms

3x = 65cm - 20cm

3x = 45cm

Divide both sides by 3

3x/3 = 45cm/3

x = 15cm

The longest side of the triangle =( x+12cm)

= (15+12)cm= 27cm

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