Question

The shortest path from point A to point B goes through a pond. To avoid
the pond, you must walk straight 23 meters along one edge of the pond,
then take a 90-degree turn, and again walk straight 57 meters along
another edge of the pond to reach point B. If you could walk through the
pond, what would be the distance from point A to point B?

Answer 1

Answer:

21.73

Step-by-step explanation:

use the Pythagorean Theorem:  AC2 + CB2 = AB2   --->   412 + 342  =  AB2 -->2837 =  AB2   -->   AB =  53.3

A to C to B =  41 + 34 = 75 meters.

A to B : 75 - 53.3 = 21.7 meters.

Answer 2

If you could walk through the pond, the distance from point 'A' to point 'B' will be 61.4 meters.

We have two points 'A' and 'B' and a pond between them.

We have to find the distance between point 'A' and 'B', if we could walk through the pond and not avoid it.

What is Pythagoras theorem?

According to the Pythagoras theorem : for a right angled triangle - $(hypotenuse)^{2} = (perpendicular)^{2} + (base)^{2}$

If we avoid the pond, than the path you will be following is the path AOB shown in the figure. However, if you decide to walk through the pond, then it can be easily seen from the figure that you will be travelling across the hypotenuse of right-angled triangle Δ AOB. Therefore, using the Pythagoras theorem in Δ AOB -

$(AB)^{2} = (AO)^{2}+(OB)^{2} \\(AB)^{2} = (23)^{2} + (57)^{2} \\(AB)^{2} = 3778\\(AB)=\sqrt{3778} \\(AB) = 61.4\;meters$

Hence, if you could walk through the pond, the distance from point 'A' to point 'B' will be 61.4 meters.

To solve more questions on Pythagoras theorem, visit the following link - https://brainly.com/question/14536245

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