Question

If the base of a triangle is four times it's height and if the area of the triangle is 242 square millimeters can you find it's base and height?

Answer 1

$h-the\ height \\a-the\ base\ \ \ \wedge\ \ \ a=4h\\A-area\ of\ a\ triangle\ \ \ \wedge\ \ \ A=242\ [mm^2]\\ \\A= \frac{1}{2} \cdot a\cdot h=\frac{1}{2} \cdot 4h\cdot h=2h^2\ \ \ \Rightarrow\ \ \ 2h^2=242\\ \\h^2=121\ \ \ \wedge\ \ \ h>0\ \ \ \Rightarrow\ \ \ h=11\ [mm]\ \ \ \Rightarrow\ \ \ a=44\ [mm]$