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The perimeter of this triangle is not more than 30 cm. 2n+3 cm, 2n+2 cm, n cm
a. Write an inequality to show this.
b. Solve the inequality.
c. What are the largest possible lengths of the sides?



Answer :

adioabiola

The inequality to represent the perimeter of the triangle is given by (2n + 3) + (2n + 2) + n ≤ 30

  • The solution to the inequality is n ≤ 5
  • The largest possible lengths of the sides is 13 cm

Inequality to represent the perimeter of a triangle

  • Perimeter of the triangle = not more than 30 cm
  • Side a = (2n + 3)cm
  • Side b = (2n + 2) cm
  • Side c = n cm

Side a + side b + side c ≤ perimeter of the triangle

(2n + 3) + (2n + 2) + n ≤ 30

  • open parenthesis

2n + 3 + 2n + 2 + n ≤ 30

5n + 5 ≤ 30

substract 5 from both sides

5n ≤ 30 - 5

5n ≤ 25

  • divide both sides by 5

n ≤ 25/5

n ≤ 5 cm

The largest possible lengths of the sides is:

Side a = (2n + 3)cm

= 2(5) + 3

= 10 + 3

= 13 cm

Side b = (2n + 2) cm

= 2(5) + 2

= 10 + 2

= 12 cm

Side c = n cm

= 5 cm

So therefore, the largest possible length of the triangle is 13 cm

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