# Algebra

posted by .

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)

## Similar Questions

1. ### math

a corner lot that was originally square lost 185m^2 area when one of the adjacent streets was widened by 3m and the other was widened by 5m. find the new dimensions of the lot.(hint:let x equal the length of a side of the original …
2. ### math

i need help in solving these 2 problems...please help..thank you... Your home is built on a square lot. To add more space to your yard, you purchase an additional 4 feet along the side of the property. The area of the lot is now 9600 …

A corner lot that originally was square lost 185 m 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.
4. ### algebra

A square plot of land has a building 60ft long and 40ft wide at one corner. The rest of the land outside the building forms a parking lot. If the parking lot has area 12,000ft^2, what are the dimensions of the entire plot of land?
5. ### math

A triangular lot sits at the corner of two streets that intersect at an angle of 63 degrees. One street side of the lot is 35m and the other is 47m. how long is the back of the lot, to the nearest metre?
6. ### algebra

a local grocery store has plans to construct a rectangular parking lot that is bordered on one side by a highway. there are 1280 feet of fencing avaliable to enclose the other three sides. find the dimensions that will maximize the …
7. ### math

a lot owner owns a corner lot , 60mx80m, .find the dimensions x, y of the largest rectangular building he can built pn his lot?
8. ### College Algebra

The parking lot is 25 by 40 feet. The owner wants to enlage the parking lot by paving an equal width strip on the north side and east side of the lot, sot hat the new lot will be twice the area of the old one. Find the equation which …
9. ### diff calculus

1.) triangular corner lot has perpendicular sides of lengths 120 feet and 160 feet. Find the dimensions of the largest rectangular building that can be constructed on the lot with sides parallel to the streets.
10. ### algebra

A rectangular lot is bordered on one side by a stream and on the other three sides by 600m of fencing. Find the dimensions of the lot if area is a maximum.

More Similar Questions