Write down the expression for the perimeter of the triangle mnk and simplify it if: a) mn = a cm, NK is 14 cm

Write down the expression for the perimeter of the triangle mnk and simplify it if: a) mn = a cm, NK is 14 cm less than MN, and KM is 3 times more than NK; b) mn = b cm, NK is 25 cm more than MN, and KM is 4 times more than NK;

a) We know that MN = a cm;

NK is 14 more, then we express it as (a – 14) cm;

KM is 3 times more than NK, then we express it as (3 * (a – 14)) cm.

Knowing that the perimeter of a triangle is the sum of all its sides, then:

P = a + (a – 14) + (3 * (a – 14)) = a + a – 14 + 3a – 42 = 5a – 56 (cm).

b) We know that MN = b cm;

NK is 25 more than MN, then we express it as (b + 25) cm;

KM is 4 times more than NK, then we express it as (4 * (b + 25)) cm.

Then:

P = b + (b + 25) + (4 * (b + 25)) = b + b + 25 + 4b + 100 = 6b + 125 (cm).