SOLUTION: please help me with my assignment. thank you.
show solutions and drawing.
1.a parallelogram has an area of 720 sq.cm. and a perimeter of 152 cm. one of the interior angles of the
Algebra ->
Parallelograms
-> SOLUTION: please help me with my assignment. thank you.
show solutions and drawing.
1.a parallelogram has an area of 720 sq.cm. and a perimeter of 152 cm. one of the interior angles of the
Log On
Question 815745: please help me with my assignment. thank you.
show solutions and drawing.
1.a parallelogram has an area of 720 sq.cm. and a perimeter of 152 cm. one of the interior angles of the parallelogram is 30 degrees. find the length of sides of the parallelogram.
2. a bench 2 ft. wide surrounds a statue with circular base. the area of the bench is 24π sq.ft. what is the diameter of the base of the statue. Found 2 solutions by ewatrrr, rothauserc:Answer by ewatrrr(24785) (Show Source):
Hi,
parallelogram has an area of 720 sq.cm. and a perimeter of 152 cm.
one of the interior angles of the parallelogram is 30 degrees , h = a/2
A = b = 1440/a
P = 2b + 2a = 152cm
0r b + a = 76
a^2 - 76a + 1440 = 0
(a-40)(a-36) = 0, a = 40 0r a = 36
Parallelogram is 40cm by 36cm
θ radians sin θ cos θ tan θ
0° 0 0 1 0
30° π/6 1/2 √3/2 √3/3
45° π/4 √2/2 √2/2 1
60° π/3 √3/2 1/2 √3
90° π/2 1 0 ─
You can put this solution on YOUR website! Start with what we know about a parallelogram
- opposite sides are parallel
- opposite sides are of equal length
- opposite interior angles are equal (angles "a" are equal, angles "b" are equal)
- angles "a" and "b" add up to 180 degrees
1) area (A) of parallelogram is the base (b) times the height (h), the perimeter is 2 times (b+s), sin(30) = h/s = 1/2 and s = 2*h
720 = b*h
152 = 2*(b+s)
substitute for s in second equation
152 = 2*(b+2h)
solve second equation for h, h = (76 - b) / 2
substitute for h in first equation
720 = b * (76 - b) / 2
1440 = 76b - b^2
put equation in standard form
b^2 -76b +1440 = 0
use quadratic formula to solve for b
b = (76+square root(76^2 - 4*1*1440)/(2*1)
b = (76 + 2.45) / 2 = 39.2 cm or
b = (76 - 2.45) / 2 = 36.8 cm
note that h = (76 - 39.2) / 2 = 18.4 cm or
h = (76 - 36.8) / 2 = 19.6 cm
s = 2 * 18.4 = 36.8 cm or
s = 2 * 19.6 = 39.2, therefore
base is 39.2 cm and side is 36.8 cm or
base is 36.8 cm and side is 39.2 cm
2) we know the area of a circle is equal to pi * radius(r)^2, where r is radius of the base of the statue
area of the bench = 24*pi = pi*(r+2)^2 - pi*r^2
divide both sides of the = by pi
24 = r^2+4r+4 - r^2
24 = 4r +4
4r = 20
r = 5 and
diameter of base of statue = 5 *2 = 10 feet
