Your friend claims that if you dilate a rectangle by a scale factor of three, then the area of your new rectangle will also increase by a factor of three. Is your friend correct? Explain your reasoning in at least four complete
sentences

No, the area of the dilated triangle will increase by a factor of 9

Step-by-step explanation:

When the scale factor by which the dimensions is dilated = 3, we have;

The original length of base = b

The base length of the dilated triangle = 3×b

The original height of the the triangle = h

The height of the dilated triangle = 3×h

The original area of the triangle = 1/2 × base × height = 1/2×b×h

The area of the dilated triangle = 1/2 × base of dilated triangle × height of dilated triangle

∴ The area of the dilated triangle = 1/2× 3 × b × 3× h  = 9×1/2× b×h

Which gives;

The area of the dilated triangle  = 3²×1/2× b×h= (Scale factor)²× The original area of the triangle.

From 3² = 9, we have;

The area of the dilated triangle = 9 × The original area of the triangle.

Therefore;

The area of the dilated triangle will increase by a factor of 9.