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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

Respuesta :

The perimeter of a triangle is given by:

[tex]P=s_1+s_2+s_3=12[/tex]

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

[tex]P^{\prime}=3s_1+3s_2+3s_3=3(s_1+s_2+s_3)=3(12)=36_{}_{}[/tex]

Therefore the new triangle will have a perimeter of 36.

Now, the original area is given by:

[tex]A=\frac{1}{2}bh=6[/tex]

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

[tex]A=\frac{1}{2}(3b)(3h)=9(\frac{1}{2}bh)=9(6)=54[/tex]

Therefore the new area is 54.

Wiith this we conclude that the answer is 3.

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