Question

A woman travels 7 km due north,
then goes 4 km due east and then 4 km due south.How far is she from the starting point?

Answer 1

hi

ur answer is there in the photo given below

hope it helps u

:)

Answer 2

Given:

Distance travelled by the woman towards North = 7 km.

Distance travelled towards East = 4 km.

Distance travelled towards South = 4 km.

To Find:

In order to find out how far is the woman from the starting point, we have to draw a rough plot of her journey.

The distance covered by the woman is the shortest distance between the starting and the ending point.

Solution:

Rough picture of the path followed by the woman is plotted in Figure 1, in which point A is the starting point and point D is the end point.

The starting point and end point is connected through a line AD, whose length itself gives the answer.

In order to find out the answer, at first a perpendicular is drawn from point D to the line AB. Now, we have a square BCDE and a right triangle AED as in Figure 2.

The hypotenuse of the triangle AED, that is, the length DA is the shortest distance between the starting point and the end point.

Using Pythagoras Theorem,

$(Hypotenuse)^{2} = (Base)^{2} + (Altitude)^{2}.$

Applying above theorem for triangle AED we get,

$(DA)^{2} = (AE)^{2} + (ED)^{2}$

Substituting the values for AE and ED the above equation becomes,

$(DA)^{2} = (3)^{2} + (4)^{2}\\(DA)^{2} = 9 + 16 = 25\\DA = \sqrt{25} = 5 km.$

Hence, the woman is 5km away from the starting point.

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