The perimeter of a triangle is 79.75 inches. the second side of the triangle is half as big as the first side. the third side is 7.25 in. greater thatn the first. what is the length of the longest side?

The triangle has 3 sides: a, b, c

The perimeter of the triangle is 79.75 inches: → a + b + c = 79.75

The second side of the triangle is half as big as the first side: → b = a/2

The third side is 7.25 inches greater than the first side: → c = a + 7.25

a + b + c = 79.75 → but you know that: c = a + 7.25

a + b + (a + 7.25) = 79.75

a + b + a + 7.25 = 79.75

2a + b = 79.75 - 7.25

2a + b = 72.5 → but you know that: b = a/2

2a + (a/2) = 72.5

(4a/2) + (a/2) = 72.5

(4a + a) / 2 = 72.5

5a/2 = 72.5

5a = 2 * 72.5

a = (2 * 72.5) / 5

→ a = 29

b = a/2

b = 29/2

→ b = 14.5

c = a + 7.25

c = 29 + 7.25

→ c = 36.25

I guess the answer is 36.05 inches ...