# 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

ft^{2} 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/sec^{2} 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/sec^{2}, 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 x^{3} − 1 = (x −
1)(x^{2} + x + 1)

so these complex cube roots satisfy the quadratic equation x^{2} + 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.

Prev | Next |