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