Question

tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards. what is the length of the diagonal, in yards, that tanya runs? 10 yards 50 yards 46.7 yards 26.5 yards

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle (formed by length, width and diagonal of the rectangle), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 30\) (width), \(b = 40\) (length) and \(c\) is the diagonal.
So, \(c=\sqrt{30^{2}+40^{2}}\).

Step2: Calculate squares

\(30^{2}=900\) and \(40^{2}=1600\). Then \(30^{2}+40^{2}=900 + 1600=2500\).

Step3: Find the square root

\(c=\sqrt{2500}\). Since \(50\times50 = 2500\), \(c = 50\).

Answer:

50 yards