Question

practice - radical equations and applications
18 points possible answered: 12/18
question 17
given a field 143 feet by 66 feet, how far is it to walk from one corner of the field to the opposite corner, to the closest tenth of a foot?
answer: the distance is approximately feet.

Explanation:

Step1: Apply Pythagorean theorem

The field is rectangular. Let \(a = 143\) and \(b=66\). The distance \(d\) from one corner to the opposite corner (diagonal) is given by \(d=\sqrt{a^{2}+b^{2}}\) (Pythagorean theorem \(c = \sqrt{a^{2}+b^{2}}\) for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\)). So \(d=\sqrt{143^{2}+66^{2}}\).
First, calculate \(143^{2}=143\times143 = 20449\) and \(66^{2}=66\times66=4356\). Then \(a^{2}+b^{2}=20449 + 4356=24805\).

Step2: Calculate the square root

\(d=\sqrt{24805}\approx157.5\) (using a calculator to find \(\sqrt{24805}\)).

Answer:

\(157.5\)