The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x.
Write the solution for this as an ordered pair.
To find the measures of x and y, we can set up a system of equations based on the given information.
Let's denote the measure of one side of the triangle as x and the other two sides as x and y. We know that the perimeter of the triangle is 46, so we can write the equation:
x + x + y = 46
Since y is 4 centimeters longer than x, we can also write the equation:
y = x + 4
Now we have a system of two equations:
1) x + x + y = 46
2) y = x + 4
To solve this system, we can substitute the value of y from equation 2 into equation 1.
Substituting y = x + 4 into equation 1, we get:
x + x + (x + 4) = 46
Combining like terms, we have:
3x + 4 = 46
Now we solve for x:
3x = 42
Dividing both sides by 3, we get:
x = 14
Substituting x = 14 into equation 2, we find:
y = 14 + 4 = 18
Therefore, the solution is (x, y) = (14, 18).