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?
Question
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:
16 cm
Step-by-step 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
[tex] \therefore \: x + (x + 2) + (x + 4) = 42 \\ 3x + 6 = 42 \\ 3x = 42 – 6 \\ 3x = 36 \\ x = \frac{36}{3} \\ x = 12 \\ \\ \because \: longest \: side = x + 4 \\ \therefore \: longest \: side = 12 + 4 \\ \red{ \bold{ \therefore \: longest \: side = 16 \: cm}} \\ [/tex]