Question

in the diagram, ( ab = 10 ) and ( ac = 2sqrt{10} ). what is the perimeter of ( \triangle abc )?
10 units
( 10 + 2sqrt{10} ) units
20 units
( 20 + 2sqrt{10} ) units

Explanation:

Step1: Find the length of \(BC\)

Since \(B(-5,-2)\) and \(C(5,-2)\), using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) or observing that \(y\) - coordinates are the same.
\(BC=\vert5-(-5)\vert=\vert5 + 5\vert = 10\)

Step2: Calculate the perimeter of \(\triangle ABC\)

The perimeter \(P\) of a triangle is \(P=AB + BC+AC\).
Given \(AB = 10\), \(AC=2\sqrt{10}\), and \(BC = 10\)
\(P=10+10 + 2\sqrt{10}=20 + 2\sqrt{10}\)

Answer:

\(20 + 2\sqrt{10}\) units