Respuesta :
The ratio of the areas is the square of the ratio of the corresponding sides and this can be determined by using the Pythagorean theorem and the formula of the area of the triangle.
Given :
- A right triangle has legs 15 inches and 12 inches.
- Every dimension is multiplied by 1/3 to form a new right triangle with legs 5 inches and 4 inches.
The base of the right triangle whose legs are 15 inches and 12 inches is calculated by using the Pythagorean theorem:
[tex]\rm 15^2=12^2+B^2[/tex]
B = 9 inches
The area of the right triangle whose legs are 15 inches and 12 inches is given by:
[tex]\rm A = \dfrac{1}{2}\times 9 \times 15[/tex]
A = 67.5 [tex]\rm inch^2[/tex]
The base of the right triangle whose legs are 5 inches and 4 inches is calculated by using the Pythagorean theorem:
[tex]\rm 5^2=4^2+B^2[/tex]
B = 3 inches
The area of the right triangle whose legs are 5 inches and 4 inches is given by:
[tex]\rm A' = \dfrac{1}{2}\times 3 \times 5[/tex]
A' = 7.5 [tex]\rm inch^2[/tex]
Now, the ratio of the area is calculated as:
[tex]\rm \dfrac{A}{A'}=\dfrac{67.5}{7.5}=9[/tex]
Therefore, the correct option is A) The ratio of the areas is the square of the ratio of the corresponding sides.
For more information, refer to the link given below:
https://brainly.com/question/11897796
