Answer
30 feet for width, 10 feet for height
Work Step by Step
$100x^2+225y^2=22500$
$(100x^2+225y^2)/22500=22500/22500$
$100x^2/22500+225y^2/22500 =1$
$x^2/225 + y^2/100 = 1$
$x^2/15^2 + y^2/10^2 = 1$
An ellipse in the form $x^2/a^2 + y^2/b^2 = 1$ has x-intercepts at $(±a,0)$ and y-intercepts at $(0, ±b)$.
$b=10$, $a=15$
The x-intercepts are $(-15, 0)$ and $(15,0)$, and the y-intercepts are $(0, 10)$ and $(0, -10)$.
Since the x-intercepts are the furthest points on that axis, we add the absolute values of the intercepts to get the width of the arch.
For the height, we use the absolute value of the y-intercept.
$15+15=30$
$abs(-10)=10$
