Question

Given: m angle P equals open parentheses 5 x minus 27 close parentheses degree, m angle Q equals open parentheses 4 x minus 7 close parentheses degree, and m angle R equals open parentheses 3 x plus 10 close parentheses degree. Which side in increment P Q R is the shortest?

Answer 1

Answer: Side QR

Explanation: The sum of a triangle internal angles is 180°. So to determine the angles, we calculate x:

5x - 27 +4x - 7 + 3x + 10 = 180

12x = 204

x = 17

With x, solve for the angles:

m∠P = 5(17) - 27 = 58

m∠Q = 4(17) - 7 = 61

m∠R = 3(17) + 10 = 61

The relationship between angles and sides in any triangle:

• the largest angle is opposite the largest side;
• the middle angle is opposite to the middle-sized side;
• the shortest angle and side are opposite to each other;

So, the shortest side of PQR is the side opposite to the shortest angle.

The shortest angle is m∠P = 58°. Therefore, the shortest side is QR