the base of an isosceles triangle is 5m less than 4 times the length of a side. The perimeter is 67m. Find the length of each side and the base. My answers for the equal side lengths are 24 and the base is 19. What is the proper way to show work since i used guess and check?

Your problem is impossible. You know that any side of a triangle is less than the sum of the other two sides.

base: b
side: s

b = 4s-5
so, 4s-5 < 2s
2s < 5
s < 2.5
But the perimeter is 67!

Maybe you meant the base is 5 less than either of the equal sides. Then we have

b = s-5

perimeter:

p = b+2s = 67

s-5 + 2s = 67
3s = 72
s = 24
b = 24-5 = 19

To find the length of each side and the base of the isosceles triangle, let's use algebraic methods instead of guess and check.

Let's denote the length of each equal side as "s" and the length of the base as "b." We're given the following information:

1. The base of the triangle is 5m less than 4 times the length of a side: b = 4s - 5

2. The perimeter of the triangle is 67m: 2s + b = 67

Now, we can solve these two equations simultaneously to find the values of s and b.

Substitute the value of b from equation 1 into equation 2:

2s + (4s - 5) = 67
6s - 5 = 67
6s = 72
s = 12

Now, substitute the value of s into equation 1 to find the value of b:

b = 4s - 5
b = 4(12) - 5
b = 48 - 5
b = 43

Therefore, the length of each equal side is 12m, and the length of the base is 43m.