Question

Triangle RJM has an area of 6 and a perimeter of12. If the triangle is dilated by a scale factor of 3centered at the origin, what are the area andperimeter of its image, triangle R'I'M"?1) area of 9 and perimeter of 152) area of 18 and perimeter of 363) area of 54 and perimeter of 364) area of 54 and perimeter of 108

Answer 1

The perimeter of a triangle is given by:

`P=s_1+s_2+s_3=12`

Now, if the triangle is dilated by a factor of 3 this means that we multiply each side by 3, then we have:

`P^(\prime)=3s_1+3s_2+3s_3=3(s_1+s_2+s_3)=3(12)=36_{}_{}`

Therefore the new triangle will have a perimeter of 36.

Now, the original area is given by:

`A=(1)/(2)bh=6`

if we dilate the triangle by a factor of three we get:

`A=(1)/(2)(3b)(3h)=9((1)/(2)bh)=9(6)=54`

Therefore the new area is 54.

Wiith this we conclude that the answer is 3.