Question

Find the value of x on this triangle

Answer 1

Look at the picture.

ΔABD and ΔBCD are similar, therefore:


`(y)/(5)=(11)/(y)\ \ \ |\cross\ multiply\\\\y^2=55\to y=√(55)`

Use Pythagorean theorem:


`x^2=5^2+(√(55))^2\\\\x^2=25+55\\\\x^2=80\to x=√(80)\\\\x=√(16\cdot5)\\\\x=√(16)\cdot\sqrt5\\\\\boxed{x=4\sqrt5}`