The lengths of the sides of triangle PQR are consecutive even integers. The perimeter of triangle PQR is 42 cm. What is the leng

Question

lutik1710 [3]

1 year ago

5

The lengths of the sides of triangle PQR are consecutive even integers. The perimeter of triangle PQR is 42 cm. What is the leng

th of the longest side?

Mathematics

1 answer:

Yuri [45] · Answer 1 · 2024-01-16T02:30:30+03:00

Yuri [45]1 year ago

6 0

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

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