in the diagram, ab = 10 and ac = 2√10. what is the perimeter of △abc?\n10 units\n10 + 2√10 units\n20…

Explanation:

Step1: Identify the given lengths of sides AB and AC.

The problem states that the length of side AB is 10 units and the length of side AC is $2\sqrt{10}$ units. $$AB = 10$$ $$AC = 2\sqrt{10}$$

Step2: Calculate the length of side BC using the distance formula.

The coordinates of point B are $(-5, -2)$ and the coordinates of point C are $(5, -2)$. The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. $$BC = \sqrt{(5 - (-5))^2 + (-2 - (-2))^2}$$ $$BC = \sqrt{(5 + 5)^2 + (-2 + 2)^2}$$ $$BC = \sqrt{(10)^2 + (0)^2}$$ $$BC = \sqrt{100 + 0}$$ $$BC = \sqrt{100}$$ $$BC = 10 \text{ units}$$

Step3: Calculate the perimeter of triangle ABC.

The perimeter of a triangle is the sum of the lengths of its three sides: $P = AB + AC + BC$. $$P = 10 + 2\sqrt{10} + 10$$ $$P = 20 + 2\sqrt{10} \text{ units}$$

Answer:

$20 + 2\sqrt{10}$ units