Two triangles are similar. The ratio of their areas is 1:4. If the height of the smaller triangle is 3 cm, how long is the corresponding height of the larger triangle, in centimeters?

Question

does this mean that i just multiply the numbers of the sides by four?

Answer 1

areas of similar figures area proportional to the square of their sides

area1/area2 = side1^2/side2^1
1/4 = side1^2/side2^2
4side1^2 = side2^2
take √ of both sides
2side1 = side2

so if one side is 3, the side of the larger square must be 6

check:
area of smaller is 3x3 = 9
area of larger is 6x6 = 36, which is in the ratio of 9/16 = 1:4

Answer 2

12