Sketch a diagram describing the given situation, and then recall the Pythagorean Theorem.
≈ 18.4 meters
Practice makes perfect
We are given that Alexi walked 27 meters south and 38 meters east to get around the lake, and her sister swam across the lake. Let's sketch a diagram describing this situation. We will name the distance across the lake d.
Since we have a right triangle in our diagram, we can solve for d using the Pythagorean Theorem. According to this theorem, the sum of the squared legs of a right triangle is equal to its squared hypotenuse. With this information, we can write an equation.
27^2+ 38^2= d^2
Let's solve the above equation. Notice that since d represents the distance, we will consider only the positive case when taking a square root of d^2.
We found that Alexi's sister swam approximately 46.6 meters.
Now we can evaluate how many meters Alexi's sister saved by swimming. To do this, we should evaluate the difference between the distance Alexi walked and the distance her sister swam.
( 27+ 38)- 46.6=18.4
Alexi's sister saved approximately 18.4 meters by swimming.
