Respuesta :
Solution
Question 1:
- The relationship between an area and its dilated image is given by:
[tex]\begin{gathered} \frac{A_2}{A_1}=k \\ \text{where,} \\ k=\text{ Dilation factor} \\ A_1=\text{Area of the original object} \\ A_2=\text{Area of the Dilated image} \end{gathered}[/tex]- We have been given the original area to be 3 and the dilation factor is 6.
- Thus, we can solve the question as follows:
[tex]\begin{gathered} \frac{A_2}{A_1}=k \\ \\ A_1=3,k=6 \\ \\ \therefore\frac{A_2}{3}=6 \\ \\ \therefore A_2=6\times3=18 \\ \\ \text{Thus, the area of the Dilated image of the triangle is 18}mm^2\text{ (OPTION C)} \end{gathered}[/tex]Question 2:
- The relationship described above also applies here, we have that:
[tex]\begin{gathered} \frac{A_2}{A_1}=k \\ \text{where,} \\ k=\text{ Dilation factor} \\ A_1=\text{Area of the original object} \\ A_2=\text{Area of the Dilated image} \end{gathered}[/tex]- The original area is 5/8 ft² and the Dilation factor is 8.
- Thus, we can solve the question as follows:
[tex]\begin{gathered} \frac{A_2}{A_1}=k \\ A_1=\frac{5}{8},k=8 \\ \\ \therefore\frac{A_2}{\frac{5}{8}}=8 \\ \\ \text{Cross multiply} \\ A_2=8\times\frac{5}{8} \\ \\ \therefore A_2=5ft^2 \\ \\ \text{Thus, the area of the dilated rectangle is 5}ft^2 \end{gathered}[/tex]Final Answer
Question 1:
The area of the Triangle is 18mm²
Question 2:
The area of the Rectangle is 5ft²
