Question

Triangle M was dilated by a scale factor of 1.2 to form triangle M. How does the area of triangle M'

relate to the area of triangle M?
A- The area of triangle M'is 0.6 times the area of triangle M.
B- The area of triangle M'is 1.2 times the area of triangle M.
C- The area of triangle M'is 1.44 times the area of triangle M.
D- The area of triangle M' is 2.4 times than the area of triangle M.

Answer 1

C- The area of triangle M'is 1.44 times the area of triangle M.

Explanation:

1.44 divided by 1.2=1.2

Answer 2

The area of triangle M is 1.44 times the area of triangle M.

Explanation:

From Geometry we remember that the area formula of the triangle is:

`A = (1)/(2)\cdot b\cdot h` (1)

Where:

`b` - Base of the triangle, dimensionless.

`h` - Height of the triangle, dimensionless.

`A` - Area of the triangle, dimensionless.

The dillation of the triangle by a scale factor means that:

`A' = (1)/(2)\cdot b'\cdot h'` (2)

`b' = k\cdot b` (3)

`h' = k\cdot h` (4)

Where:

`b'` - Dilated base of the triangle, dimensionless.

`h'` - Dilated height of the triangle, dimensionless.

`A'` - Dilated area of the triangle, dimensionless.

`k` - Dilation factor, dimensionless.

If we know that
`k = 1.2`, then the area formula for the dilated triangle is:

`A' = (1)/(2)\cdot (k\cdot b)\cdot (k\cdot h)`

`A' = k^(2)\cdot (1)/(2)\cdot b\cdot h`

`A' = k^(2)\cdot A`

Therefore, the area of triangle M is 1.44 times the area of triangle M.