Question

a gopher has dug holes in opposite corners of a rectangular yard. one length of the yard is 48 feet and the distance between the gophers holes is 73 feet. how wide is the yard? feet

Explanation:

Step1: Apply Pythagorean theorem

Let the width of the yard be \(w\). In a rectangle, the length \(l = 48\) feet and the diagonal \(d=73\) feet. By the Pythagorean theorem \(l^{2}+w^{2}=d^{2}\), so \(w^{2}=d^{2}-l^{2}\).

Step2: Substitute values

Substitute \(l = 48\) and \(d = 73\) into the formula: \(w^{2}=73^{2}-48^{2}\).
Calculate \(73^{2}=73\times73 = 5329\) and \(48^{2}=48\times48=2304\). Then \(w^{2}=5329 - 2304=3025\).

Step3: Find \(w\)

Take the square root of \(w^{2}\). Since \(w>0\), \(w=\sqrt{3025}\). And \(\sqrt{3025} = 55\).

Answer:

55