Question

two triangles are similar and have a ratio similarity of 2:5 what is the ratio of their perimeters and the ratio for the area.

Answer 1

the ratio of perimeters is equal to the ratio of sides


the ratio of areas is equal to the SQUARE of the ratio of the sides

Answer 2

do you get that @y0urpointismo0t ? would you like me to prove it? lol

Answer 3

kind of, can you?

Answer 4

let's say we have triangles...the side of one triangle is 2 and the side of the other is 5..for simplicity sake

ratio of lengths = 2: 5

perimeter of triangle 1: 2 + 2 + 2 = 6

perimeter of triangle 2: 5 + 5 + 5 = 15

ratio of perimeters = 6 : 15

if i simplify that by dividing both by 3 i get

ratio of perimeters = 2: 5 <---proven

area of triangle 1: \(\sqrt 3/2\)(i wont go through details abt that im just here to prove)

area of triangle 2: \(\frac{25\sqrt 3}{8}\)

ratio of areas = \(\frac{\sqrt 3}{2} : \frac{25\sqrt 3}{8}\)

if i rewrite it in this form: \[\large \frac{\frac{\sqrt 3}{2}}{\frac{25\sqrt 3}{8}}\]

sqrt 3 and 2 will cancel out and give us \[\large \frac{1}{\frac{25}{4}}\] simplifying this..we get \(\frac{4}{25}\)

in ratio form this is 4 : 25

4 is square of 2 and 25 is square of 5..thus proven @y0urpointismo0t