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?

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle (where the length \(l = 40\) yards, width \(w=30\) yards and diagonal \(d\) is the hypotenuse) is \(d^{2}=l^{2}+w^{2}\).
Substitute \(l = 40\) and \(w = 30\) into the formula: \(d^{2}=40^{2}+30^{2}\).
Calculate \(40^{2}=1600\) and \(30^{2}=900\). Then \(d^{2}=1600 + 900\).

Step2: Solve for \(d\)

\(d^{2}=2500\). Take the square root of both sides: \(d=\sqrt{2500}\).
Since \(\sqrt{2500}=50\) (because \(50\times50 = 2500\)).

Answer:

50 yards