Given that triangle ABC = triangle QRS, prove algebraically that the ratio of their perimeter is 1:4 if the ratio of their corresponding sides it 1:4.

Question

Please write an algebraic proof answering the following questions.

Answer 1

Because Triangle ABC is similar to Triangle QRS, we have the corresponding side lengths proportional.

let AB = x , BC = y, AC = z , because triangles are similar

QR = 4x, RS = 4y, QS = 4z.

AB/QR = BC/RS = AC/QS = 1/4

perimeter of ABC = x+y+z

perimeter of QRS = 4(x+y+z)

(perimeter of ABC) / (perimeter of QRS) = (x+y+z) / 4(x+y+z) = 1/4