Triangle DEF is rotated 90 degrees and dilated by a scale factor of 3. how do the perimeters and area's compare

Question

Perimeters  and areas compared

Answer 1

The perimeter and area has to do with the side lengths.  When you dilate the triangle by a scale factor of 3, the side lengths are 3 times as large as the original side length of the triangle.

 

If the triangle was equilateral, we can let x be the length of each side.

 

Perimeter of original = x + x + x = 3x

Perimeter of image = 3(3x) = 9x

 

Area of triangle = [(x√2)x] / 2 = (x²√2) / 2

Area of image = (3/2)(x²√2)

 

 

Take the ratio of the perimeter and area to determine how large they are to each other.