Kathy Bransbury has a large piece of land in the country. Her land is a square plot and the northern edge is in a perfect east/west line (so is the southern edge if you think about it). The road enters her land at a point on the western edge 3 miles due south of the northwest corner and 7 miles as the crow flies from the north east corner. What is the area of the land in square miles?
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Kathy Bransbury has a large piece of land in the country. Her land is a square plot and the northern edge is in a perfect east/west line (so is the southern edge if you think about it). The road enters her land at a point on the western edge 3 miles due south of the northwest corner and 7 miles as the crow flies from the north east corner. What is the area of the land in square miles?
Sketch it. Label the corners of the square ABCD clockwise from the northwest corner.
Call that point where the road enters E. Note that you've formed a handy right triangle.
By Pythagoras c2 = a2 + b2
EB2 = AE2 + AB2
72 = 32 + AB2
AB2 = 72 – 32
AB2 = 49 – 9
AB2 = 40
Since AB is a side of a square,
AB2 is the area of that square. Area of the plot is 40 mi2
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