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:
(1)
Where:
- Base of the triangle, dimensionless.
- Height of the triangle, dimensionless.
- Area of the triangle, dimensionless.
The dillation of the triangle by a scale factor means that:
(2)
(3)
(4)
Where:
- Dilated base of the triangle, dimensionless.
- Dilated height of the triangle, dimensionless.
- Dilated area of the triangle, dimensionless.
- Dilation factor, dimensionless.
If we know that
, then the area formula for the dilated triangle is:
![A' = k^{2}\cdot \frac{1}{2}\cdot b\cdot h](https://tex.z-dn.net/?f=A%27%20%3D%20k%5E%7B2%7D%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20b%5Ccdot%20h)
![A' = k^{2}\cdot A](https://tex.z-dn.net/?f=A%27%20%3D%20k%5E%7B2%7D%5Ccdot%20A)
Therefore, the area of triangle M is 1.44 times the area of triangle M.