Question

in the diagram, ab = 10 and ac = 2√10. what is the perimeter of △abc?
○ 10 units
○ 10 + 2√10 units
○ 20 units
○ 20 + 2√10 units
(diagram: coordinate grid with points a(3,4), b(-5,-2), c(5,-2) plotted, forming △abc)

Explanation:

Step1: Find length of BC

Points B(-5, -2) and C(5, -2) have same y - coordinate. So distance \( BC=\vert5 - (-5)\vert=\vert10\vert = 10\)

Step2: Calculate perimeter

Perimeter of \(\triangle ABC=AB + BC+AC\). Given \(AB = 10\), \(BC = 10\), \(AC = 2\sqrt{10}\). So perimeter \(=10 + 10+2\sqrt{10}=20 + 2\sqrt{10}\)

Answer:

\(20 + 2\sqrt{10}\) units (the option: 20 + 2√10 units)