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?
1 answer:
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.
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