# Algebra

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1) A corner lot that originally was square lost 185m^2 of area when one of the adjacent streets was widened by 3 m and the other was widened by 5 m. Find the new dimensions of the lot. (Hint: Let x = the lenght of a side of the original square lot. )

2) A running track 4 m wide goes around a soccer field that is twice as long as it is wide. At each end of the soccer field the track is a semi-circle with inner radius r. Find a formula for the area of the track in terms of *pi and r.

3a) Suppose that you plan to run once around the track described in the problem above. If you stay 0.5 m from the inner edge of the track, how far will you run? (Hint: The circumference of a circle is *2pir. Your answer will be in terms of *pi and r.)

3b) Suppose that a friend stays 0.5 m from the outer edge of the track. How much farther does your friend run than you do?

*pi = 3.14 or 22/7

• Algebra -

original square ---- > let each side be x
new sides are x-3 and x-5

so x^2 - (x-3)(x-5) = 185
x^2 - (x^2 - 8x + 15) = 185
8x - 15 = 185
x = 200/8 = 25

check:
original square was 25 by 25 , area = 625
new rectangle was 22 by 20 , area = 440
difference = 625-440 = 185
All looks good

2. I will let you do this one.

Hint: let the width of the soccer field be 2r, that way you can label the radius of the ends as r
The two semi-circular ends will constitute one whole circle. So the circular part of the track will be the "ring" formed by two circles, one of radius r, the other of radius (r-4)