Question

In the figure below, AB=AC=50, AD=52, and BC=28. Determine CD.

Answer 1

Explanation:

CD= 6

Answer 2

Check the picture below, on the left side.

since the triangle ABC is an isosceles with twin sides, if we drop a line bisecting the angle at the vertex A, we end up with a perpendicular line that cuts the "base" in two equal halves, so then

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2-a^2)=b \qquad \begin{cases} c=\stackrel{hypotenuse}{50}\\ a=\stackrel{adjacent}{14}\\ b=opposite\\ \end{cases} \\\\\\ √(50^2 - 14^2)\implies √(2500 - 196)=b\implies √(2304)=b\implies 48=b`

as you can see in the picture in red, now let's find CD.

`\stackrel{\textit{pythagorean theorem}}{√(52^2 - 48^2)=14}+CD\implies √(2704-2304)=14+CD \\\\\\ √(400)=14+CD \implies 20=14+CD\implies 6=CD`