Question

1. triangle abc has vertices at a (3, 5), b (5, 7) and c (7, 5). lisa believes that the perimeter of δabc is 12 units. why is lisa incorrect? a because ab = 2√2 units, bc = 2√2 units and ac = 4 units. b because ab = 8 units, bc = 8 units and ac = 16 units. c because ab = 2 units, bc = 2 units and ac = 2 units. d because ab = 4 units, bc = 4 units and ac = 8 units.

Explanation:

Step1: Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for side $AB$.

Given $A(3,5)$ and $B(5,7)$, then $AB=\sqrt{(5 - 3)^2+(7 - 5)^2}=\sqrt{2^2+2^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}$

Step2: Use distance formula for side $BC$.

Given $B(5,7)$ and $C(7,5)$, then $BC=\sqrt{(7 - 5)^2+(5 - 7)^2}=\sqrt{2^2+(- 2)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}$

Step3: Use distance formula for side $AC$.

Given $A(3,5)$ and $C(7,5)$, then $AC=\sqrt{(7 - 3)^2+(5 - 5)^2}=\sqrt{4^2+0^2}=4$

Step4: Analyze Lisa's error.

The perimeter of $\triangle ABC$ is $AB + BC+AC=2\sqrt{2}+2\sqrt{2}+4
eq12$. Lisa is wrong because $AB = 2\sqrt{2}$ units, $BC = 2\sqrt{2}$ units and $AC = 4$ units.

Answer:

A. Because $AB = 2\sqrt{2}$ units, $BC = 2\sqrt{2}$ units and $AC = 4$ units.