The girl walked 20m from the house towards the west, then turned north and walked 800m.

| April 29, 2021 | education

The girl walked 20m from the house towards the west, then turned north and walked 800m. After that she turned east and walked another 200m. At what distance (meters) from the house was the girl?

The path that the girl took can be represented as a rectangular trapezoid with a large base of 200 m, a smaller base of 20 m and a lateral side, which is also the height of the trapezoid, equal to 800 m.
The distance from the point at which the girl was to the house is the hypotenuse of the triangle, which is formed by the second height of the trapezoid. This height cuts off a right-angled triangle with a leg of 800 m and a leg equal to 200 m – 20 m from the trapezoid.The second leg of the triangle will be equal to 180 m.
Let’s find the length of the hypotenuse (distance to the house):
P = √ (800 ^ 2 + 180 ^ 2) = √ (640000 + 32400) = √ 672400 = 820 (m).
Answer: the distance to the house is 820 m.



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