Question

"In isosceles triangle ABC, where CA = CB, the perimeter of the triangle is 216 inches. If CA is represented as 4x + 10 inches, CB as 6x - 28 inches, and AB as 3x - 13 inches, what is the length of side AB? Please provide your answer in inches."

Answer 1

The length of side AB is 44 inches in an isosceles triangle ABC.

Step-by-step explanation:

In an isosceles triangle ABC, CA is represented as 4x + 10 inches and CB is represented as 6x - 28 inches. Since CA = CB in an isosceles triangle, we can set the expressions for CA and CB equal to each other:

4x + 10 = 6x - 28

Subtracting 4x from both sides and adding 28 to both sides, we get:

38 = 2x

Dividing both sides by 2, we find:

x = 19

Now, we can substitute the value of x back into the expression for AB to find its length:

AB = 3x - 13

Substituting x = 19:

AB = 3(19) - 13

AB = 57 - 13

AB = 44

Therefore, the length of side AB is 44 inches.