Question

In the figure below, AD=5cm, CD=12cm and points C and D are on the perpendicular bisector of segment AB. What is the perimeter of triangle ABC

Answer 1

so we know that CD is a perpendicular bisector to AB, if that's so, that means the triangle is an isosceles triangle, the hell does that mean? well, it means that AC = CB and that AD = DB.

now, we know that DB = AD = 5, and let's use the pythagorean theorem to get AC and CB.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{5}\\ o=\stackrel{opposite}{12} \end{cases} \\\\\\ AC=√( 5^2 + 12^2) \implies AC=√( 169 )\implies AC=13=CB \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{13~~ + ~~13~~ + ~~5~~ + ~~5}\implies \text{\LARGE 36}`