# To get from your house to your grandparent’s house you must avoid walking through a pond......To avoid the pond, you walk 0.5 miles south and 1.2 miles east. How many miles would be saved if it...

To get from your house to your grandparent’s house you must avoid walking through a pond...

...To avoid the pond, you walk 0.5 miles south and 1.2 miles east. How many miles would be saved if it were possible to walk through the pond?

A. 0.4 m

B. 1.69 m

C. 3.0 m

D. 6.4 m

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### 1 Answer

To reach your grandparent’s house from your house while having to avoid walking through a pond you have to walk 0.5 miles south and 1.2 miles east.

If it were possible to walk through the pond the distance you would have to travel would be given by sqrt (0.5^2 + 1.2^2). This follows from the fact that when you walk towards the south and the east you are walking in perpendicular directions. We can consider them to be the legs of a right triangle and use the Pythagorean Theorem to find the length of the hypotenuse.

sqrt (0.5^2 + 1.2^2)

=> sqrt (0.25 + 1.44)

=> sqrt (1.69)

=> 1.3

The total distance you would travel here is 1.3 m. The distance you avoid walking is:

0.5 + 1.2 - 1.3 = 1.7 - 1.3 = 0.4

**The distance you would avoid walking is given by option A or 0.4 miles.**