Question

39. Triangle ABC is an isosceles triangle.

Find the perimeter of the triangle.
Give your answer to 1 decimal place.
A
6 cm
B
15 cm
D
6 cm
C

Answer 1

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=√(c^2 - o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{6}\\ a=\stackrel{adjacent}{DC}\\ o=\stackrel{opposite}{5} \end{cases} \\\\\\ DC=√( 6^2 - 5^2)\implies DC=√( 36 - 25 ) \implies DC=√( 11 ) \\\\[-0.35em] ~\dotfill`

`\textit{since the triangle is an isosceles}\qquad BD=DC=√(11) \\\\\\ \stackrel{ \textit{\LARGE perimeter} }{√(11)+√(11)+6+6}\implies 2√(11)+12 ~~ \approx ~~ \text{\LARGE 18.6}~cm`