Question

a field is 34 yd long from end to end and 54 ft wide. if a person runs diagonally across the field from one end to the other, how far does she run?
the person runs ft.
(simplify your answer.)

Explanation:

Step1: Identify the problem as a right - triangle problem

The field's length and width form the two legs of a right - triangle, and the diagonal is the hypotenuse. Let the length $a = 34$ yards and the width $b = 54$ yards.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse. Substitute $a = 34$ and $b = 54$ into the formula: $c^{2}=34^{2}+54^{2}=1156 + 2916=4072$.

Step3: Find the value of $c$

Take the square root of 4072: $c=\sqrt{4072}=\sqrt{4\times1018}=2\sqrt{1018}\approx63.81$ yards.

Answer:

$2\sqrt{1018}\approx63.81$ yards