Applications of Quadratic Formula

Use the Quadratic Formula to solve the following giving approximate answers to the nearest thousandth
unless otherwise instructed.

1. The base of a triangle is 4 cm. longer than the height. The area is 45 sq. cm. Find the base
and height.

2. The length of a rectangular plot of land is 132 ft. longer than the width. If the area is 96133
ft2 find the length and width. Hint: the answers are integers with product 96113.

3. One leg of a right triangle is 9 cm. longer than the other. The hypotenuse is 50 cm. Find the
length of the legs to the nearest mm.

4. The late Manas Torcom, a rug dealer in Park Ridge, wanted to make a rug in the shape of a
regular octogon (8 sided figure, all sides the same length) from a square 2 yards (72 inches)
to a side by cutting isosceles triangles off of each corner of the square . What should the
dimensions of each triangle be and what is the length of each side of the resulting octogon?
Give answers as mixed numbers to nearest 1/8 inch.

5. Dave and Dick, working together, tile a large floor in 30 hours. If they worked alone it
would take Dick 5 hours longer than Dave to do the job. How long would it take each
working alone? Hint: if it takes Dave t hours and Dick r hours then the formula would be

6. An object is thrown upwards from the roof of a building. The the height above the ground in
meters at time t is given by the equation

where v is the initial upwards velocity in meters per second, s is the height in meters
above ground level of the release point and g is the acceleration of gravity which averages
9.8 m/sec2 on earth but varies slightly from location to location, and t is time in seconds
from the release time.

Given that in this particular instance g = 9.78m/sec2, v = 8.24m/sec and s = 15.72m
find how many seconds after release will the object hit the ground? Give answer to nearest
hundredth of a second.

7. In addition to itself , the number 1 has two complex cube roots . Find them. Hint: You need
to solve x 3 = 1 for all solutions. But note the factorization x3 − 1 = (x − 1)(x2 + x + 1)
so these complex cube roots satisfy the quadratic equation x2 + x + 1 = 0. Give exact and
approximate answers, to 4 decimal places , for these cube roots. Check!

8. The golden mean is an important irrational ( not a fraction ) number in mathematics . This
positive number g has the property that g 2 = g + 1. Give exact and approximate values, to 7
decimal places , for g.

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