The first side is triple the second side and the third side is five times the second side. What are the sides of the triangle if the perimeter is 72ft?
a = 3 b
c = 5 b
a + b + c = 72
3 b + b + 5 b = 72
9 b = 72
b = 8
so
a = 24 and c = 40
To solve this problem, let's start by assigning variables to the sides of the triangle. Let's say that the second side is represented by "x" ft.
According to the problem, the first side is triple the second side, so the first side would be 3x ft.
Similarly, the third side is five times the second side, so the third side would be 5x ft.
Now, we can set up an equation to represent the perimeter of the triangle, which is the sum of all three sides:
Perimeter = first side + second side + third side
72 ft = 3x ft + x ft + 5x ft
To solve this equation, we can combine like terms:
72 ft = 9x ft
Next, we can isolate x by dividing both sides of the equation by 9:
72 ft / 9 = 9x ft / 9
8 ft = x ft
So, the second side of the triangle is 8 ft.
Now we can find the other sides:
First side = 3x = 3(8 ft) = 24 ft
Third side = 5x = 5(8 ft) = 40 ft
Therefore, the sides of the triangle are 24 ft, 8 ft, and 40 ft.