Is the triangle equilateral, isosceles, or scalene?
Here's the work given:
(7x - 10)° + (6x + 8)° + (4x + 8)° = 360 → 17x = 360
=
x = 360/ 17 → x ≈ 21
QP = 7(21) - 10 → 137 - 10 → 127
PR = 6(21) + 8 → 134 + 8 → 142
QR = 4(21) + 8 → 92 + 8 → 100
We can now determine the type of triangle using the side lengths:
Since all three sides of the triangle have different lengths, it is a scalene triangle.
Based on the given work, we can determine the lengths of the sides of the triangle:
QP = 127
PR = 142
QR = 100
To determine if the triangle is equilateral, isosceles, or scalene, we need to check the lengths of the sides:
In an equilateral triangle, all three sides are equal.
In an isosceles triangle, two sides are equal.
In a scalene triangle, no sides are equal.
Since QP ≠ PR ≠ QR, we can conclude that the triangle is scalene.