Question

A triangle has one side that measures x, and the other two sides each measure 4 inches less than x. The perimeter is 19 inches.

What is the measure of x?

9
5
3
2

Answer 1

Let the sides be x, x-4, x-4. Then perimeter: x + 2(x-4) = 19
=> 3x - 8 = 19
=> 3x = 27
=> x = 9.

(Checks: other sides 5 and 5, triangle inequality holds.)