Question

The lengths of the sides of a
triangle are
Find the value of x so that the
triangle is isosceles.
(2 points)
3x, 5x − 12, and x + 20.

Answer 1

To determine if a triangle is isosceles, we need two sides to be of equal length.

Given:
Side 1: 3x
Side 2: 5x - 12
Side 3: x + 20

For a triangle to be isosceles, two sides must be of equal length. Therefore, we can set up two equations:

3x = 5x - 12 (Side 1 equal to Side 2)
5x - 12 = x + 20 (Side 2 equal to Side 3)

Solving the first equation:
3x = 5x - 12
12 = 2x
x = 6

Substitute x = 6 into the second equation:
5(6) - 12 = 6 + 20
30 - 12 = 26
18 = 26

Since the second equation is not true, it means that the triangle cannot be isosceles with the values given.