Question

The lengths of the sides of triangle PQR are consecutive even integers. The perimeter of triangle PQR is 42 cm. What is the length of the longest side?

Answer 1

16 cm

Explanation:

Let the three consecutive even integers representing the sides of the triangle PQR be x, (x +2) and (x + 4).

Since, perimeter of triangle PQR = 42 cm

`\therefore \: x + (x + 2) + (x + 4) = 42 \\ 3x + 6 = 42 \\ 3x = 42 - 6 \\ 3x = 36 \\ x = (36)/(3) \\ x = 12 \\ \\ \because \: longest \: side = x + 4 \\ \therefore \: longest \: side = 12 + 4 \\ \red{ \bold{ \therefore \: longest \: side = 16 \: cm}} \\`