The value of the scale factor is 3. Then the height and area of the triangle ΔABC will be 9 ft and 54 square ft.
What is dilation?
Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.
The area of the triangle ΔDEF is 6 square ft. And the base length of the triangle ΔDEF is 4 ft.
The area of the triangle is given as
[tex]\rm Area = \dfrac{1}{2} \times bh\\\\[/tex]
Then the height of the triangle ΔDEF will be
[tex]\rm 6 = \dfrac{1}{2} \times 4 \times h\\\\h = \dfrac{12}{4}\\\\h = 3[/tex]
Then the scale factor will be
[tex]\rm SF = \dfrac{12}{4} = 3[/tex]
Then the height of the triangle ΔABC will be
[tex]\rm \dfrac{H}{3} = 3\\\\H \ = 9[/tex]
Then the area of the dilated triangle ΔABC will be
[tex]\rm Dilated \ Area = \dfrac{1}{2} \times 12 \times 9\\\\Dilated \ Area = 54 \ ft^2[/tex]
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ1
