Question

mirlande routinely bicycles across a rectangular parking lot on her way to work. if the lot is 320 ft long and 240 ft wide, how far does mirlande travel when she rides across the lot diagonally?

mirlande travels \\(\square\\) ft when she rides across the lot diagonally.
(simplify your answer.)

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 320\) (length of the rectangle), \(b=240\) (width of the rectangle), and \(c\) is the length of the diagonal.
Substitute \(a = 320\) and \(b = 240\) into the formula: \(320^{2}+240^{2}=c^{2}\).
Calculate \(320^{2}=320\times320 = 102400\) and \(240^{2}=240\times240=57600\).
Then \(102400 + 57600=c^{2}\), so \(c^{2}=160000\).

Step2: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{160000}\).
Since \(\sqrt{160000}=\sqrt{400\times400}\), \(c = 400\).

Answer:

\(400\)