Ellen can walk home from school from by either two routes. one takes her along two adjacent sides of a rectangular park whose length is 20 meters more than its width. the other route is a short cut long the diagonal of the rectangle. if the diagonal route is 40 meters shorter than the other route, what are the exact dimensions of the park?

The exact dimensions of the park is 80 meters by 60 meters.

Step-by-step explanation:

Let the width of the rectangular park is W meters, then its length will be (W + 20) meters.

Now, given that the diagonal route is 40 meters shorter than the other route.

Hence,

⇒

Now, squaring both sides we get,

(2W - 20)² = W² + (W + 20)²

⇒ 4w² - 80W + 400 = 2W² + 40W + 400

⇒ 2W² = 120W

⇒ W = 60 meters  

Now, length is (60 + 20) = 80 meters

Therefore, the exact dimensions of the park is 80 meters by 60 meters. (Answer)

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