Question

a gopher has dug holes in opposite corners of a rectangular yard. if the yard is 7 meters by 6 meters, how far will the gopher have to run to get from one of its holes to the other? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Apply Pythagorean theorem

The length and width of the rectangle are the two legs of a right - triangle, and the distance between the opposite corners is the hypotenuse. Let \(a = 7\) meters and \(b=6\) meters. According to the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse.
So \(c^{2}=7^{2}+6^{2}\).

Step2: Calculate \(a^{2}+b^{2}\)

\(7^{2}=49\) and \(6^{2}=36\), then \(a^{2}+b^{2}=49 + 36=85\). So \(c^{2}=85\).

Step3: Find \(c\)

\(c=\sqrt{85}\approx9.2\) (rounded to the nearest tenth).

Answer:

9.2