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Geometry

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Source: — Problem Solving |
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by bluementor » Sat Dec 13, 2008 12:55 pm
A slightly faster way to solve this without really getting too much into the calculations can be done the following way:

If you draw a hypotenuse to form a right angled triangle (45-45-90 triangle), you can estimate the hypotenuse to be 1.41*100.

If you were to roughly calculate the perimeter of this triangle it would be 2*100 + 1.41*100 = 341 (This is given as answer B)

Now you know that the arc (or quarter circle) section has to be just slightly longer than the hypotenuse. From the answer choices, it is safe to estimate that 357 would be the closest value.

The estimation done for this problem has been convenient because of the '100 feet' value used for the sides, as well as the answer choices.

-BM-
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by niraj_a » Sat Dec 13, 2008 2:19 pm
C

we gotta find the circumference of 1/2 of a semi-circle here, which will be the length of the curved portion.

so 2Pir = 100 * 2 * Pi = 200 Pi

1/2 of a semi circle is 1/4 of a full circle. so the circumference we need is

200 Pi * 1/4
50 * Pi
50 * 3.14 = 157

so the total circumference we need is 100 + 100 + 157 = 357
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