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

Answer:

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

Step-by-step explanation:

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

$A = \frac{1}{2}\cdot b\cdot h$ (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:

$A' = \frac{1}{2}\cdot b'\cdot h'$ (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:

$A' = \frac{1}{2}\cdot (k\cdot b)\cdot (k\cdot h)$

$A' = k^{2}\cdot \frac{1}{2}\cdot b\cdot h$

$A' = k^{2}\cdot A$

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

Answer 2

Answer:

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

Step-by-step explanation:

1.44 divided by 1.2=1.2