Question

The lengths of the sides of a triangle are 3t,5t-12, and t+20. a. Find the value (s) of t that make the triangle isosceles.

Answer 1

The values of t that make the triangle isosceles are t = 6 and t = -10.

Step-by-step explanation:

To find the value(s) of t that make the triangle isosceles, we need to identify when two sides of the triangle are equal. In an isosceles triangle, two sides are equal in length. Therefore, we can set up two equations and solve for t.

Equation 1: 3t = 5t - 12

Equation 2: 3t = t + 20

Solving Equation 1, we get t = 6. Solving Equation 2, we get t = -10. Therefore, the values of t that make the triangle isosceles are t = 6 and t = -10.

Answer 2

To make the triangle isosceles, the value of t is 6.

Step-by-step explanation:

An isosceles triangle is a triangle that has two sides of equal length. To determine the value(s) of t that make the triangle isosceles, we need to set the two sides with equal length equal to each other and solve for t.

Setting 3t = 5t - 12, we can solve for t:

3t = 5t - 12
12 = 5t - 3t
12 = 2t
t = 6

Therefore, the value of t that makes the triangle isosceles is 6.