Question

you may use your notes/cheat sheets show all steps for a grade use $\triangle abc$ for 1 & 2

1. what is the perimeter of $\triangle abc$? round to nearest tenth
2. if $\triangle abc$ is dilated by a scale factor of 2, which of the following will be true?

a. $\overline{ac} = 6$ and $m \angle a = 40^\circ$
b. $\overline{ac} = 12$ and $m \angle a = 80^\circ$
c. $\overline{ac} = 6$ and $m \angle a = 80^\circ$
d. $\overline{ac} = 12$ and $m \angle a = 40^\circ$

Explanation:

Step1: Identify side lengths from grid

From the grid, $AC = 6$, $BC = 4$.

Step2: Calculate hypotenuse $AB$

Use Pythagorean theorem:
$$AB = \sqrt{AC^2 + BC^2} = \sqrt{6^2 + 4^2} = \sqrt{36 + 16} = \sqrt{52} \approx 7.2$$

Step3: Compute perimeter

Sum all side lengths:
$$\text{Perimeter} = AC + BC + AB = 6 + 4 + 7.2$$

Step4: Analyze dilation for Q2

Dilation scales side lengths by 2: $AC_{\text{new}} = 6 \times 2 = 12$. Angles stay unchanged, so $m\angle A = 40^\circ$.

Answer:

1. 17.2
2. D. $\overline{AC} = 12$ and $m < A = 40^\circ$