Question

explain how you would find the distance xy across the lake shown below, and then find xy
which of the following explains how to find the distance xy?
a. find the length of the hypotenuse with side lengths 100 m and 200 m by using the pythagorean theorem. this is the length of side xy
b. draw a perpendicular segment from y to the segment representing 200 m. then draw the segment xy. a right triangle is formed with side lengths 100 m and 150 m. use the pythagorean theorem to find xy
c. add the lengths of all the sides given and divide by 4.
d. find the length of the hypotenuse with side lengths 50 m and 100 m by using the pythagorean theorem. then subtract the length 200 m. this is the length of side xy

Explanation:

Step1: Analyze the figure

We need to form a right - triangle to apply the Pythagorean theorem. If we draw a perpendicular segment from \(Y\) to the segment representing \(200m\), the base of the right - triangle is \(200 - 50=150m\) and the height is \(100m\).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 100m\), \(b = 150m\) and \(c=XY\).

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Answer:

B. Draw a perpendicular segment from \(Y\) to the segment representing \(200m\). Then draw the segment \(XY\). A right triangle is formed with side lengths \(100m\) and \(150m\). Use the Pythagorean theorem to find \(XY\)