Answer:
The perimeter of the triangle is 38 cm.
Explanation:
The problem describes an isosceles triangle, which means two sides of the triangle are equal. Let’s denote the equal sides as 3x - 5 and 19 - x, and the base of the triangle as 2x.
To find the perimeter of the triangle, we first need to solve for x using the equation 3x - 5 = 19 - x.
Here are the steps to solve for x:
Add x to both sides of the equation: 4x - 5 = 19.
Add 5 to both sides of the equation: 4x = 24.
Divide both sides of the equation by 4 to solve for x: x = 6.
Now that we have x = 6, we can substitute x into the expressions for the sides of the triangle to find their lengths:
The length of the equal sides is 3x - 5 = 3*6 - 5 = 13 cm.
The length of the base is 2x = 2*6 = 12 cm.
Finally, we can calculate the perimeter P of the triangle by adding up the lengths of all sides:
P = 2*(3x - 5) + 2x = 2*13 + 12 = 38 cm.
So, the perimeter of the triangle is 38 cm.
Hope it Helps!