Answer:
PQ = 43
Explanation:
In a triangle, adding three things and making it equal to 180 works for the angles. The sum of the measures of the angles of a triangle is 180 deg.
In this problem, you are not asked about angles. You are asked about sides. You are told the triangle is an isosceles triangle. That means at least two sides are congruent. Congruent sides have equal lengths. The problem tells you which two sides are congruent. Each side has a length written as an expression. Set the expressions of the congruent sides equal and solve for x.
The two congruent sides are segment PQ and segment PR.
3x + 10 = 5x - 12
Subtract 5x from both sides.
-2x + 10 = -12
Subtract 10 from both sides.
-2x = -22
Divide both sides by -2.
x = 11
Now we know x = 11. PQ = 3x + 10. We let x = 11 in the expression and evaluate it.
PQ = 3x + 10 = 3(11) + 10 = 33 + 10 = 43
PQ = 43