Question

A triangle has side lengths of 5 inches, 12 inches, and 15 inches. Every dimension is multiplied by 1/5 to form a new triangle. How is the ratio of the perimeters related to the ratio of corresponding sides?

Answer 1

a = 5 in

b = 12 in

c = 15 in

the lengths of the sides a, b and c

the perimeter is P = a + b + c = 5 + 12 + 15 = 32 in

let the dimensions of the new triangle be

a1 = (1/5)*5 in

b1 = (1/5)*12 in

c1 = (1/5)*15 in

the perimeter is P1 = a1 + b1 + c1 = (1/5)5 + (1/5)12 + (1/5)15 = (1/5)(5 + 12 + 15) = (1/5)P1

P1 = (1/5)P

P1/P = 1/5 = a/a1 = b/b1 = c/c1

the ratio of the perimeters is equal to the ratio of the corresponding sides.