Answer:
The length is 15 miles and the width is 5 miles.
Step-by-step explanation:
The rectangle has two dimensions, width w and length l.
The area is given by the following formula:
\(S = wl\).
In this problem, we have that:
The width is 10 miles less than its length. This means that
\(w = l - 10\)
The area is 75 square miles. So
\(wl = 75\)
\((l - 10)l = 75\)
\(l^{2} - 10l - 75 = 0\).
\(l = 15\) and \(l = -5\).
We cannot have negative dimensions. This means that the length is 15 miles and the width is 5 miles.
