If the sides of a triangle are tripled, by what number would the area be multiplied?
I Don't understand the question so I don't know how to show the work.
let the base of the first triangle be b
let the height of the first triangle be h
area of first triangle = (1/2)bh
If the sides are tripled the new triangle is similar to the first one, and the height will also be tripled
new base = 3b
new height = 3h
new area = (1/2)(3b)(3h) = (1/2)(9bh)
which is 9 times as big as the first one,
illustrating the concept that the ratio of similar triangles is proportional to the square of their corresponding sides.
that is 1^2 : 3^2 = 1 : 9