A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. She wants the area to be 225 square yards. The situation is modeled by the equation . Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard.

Question

anonymous · Answer

http://www.mathsisfun.com/geometry/trapezoid.html Let a be the short side, b be the long side and h be the height. Solve the following for a b and h:$$\left\{a=h+3,b=h+7,\frac{a+b}{2}h=225\right\} $$

kropot72 · Answer

The formula for the area of a trapezium is as follows:
$$area=\frac{1}{2}(a+b)h$$
Let a be the shorter base. Then a = h + 3.
Let b be the longer base. Then b = h + 7.
Substituting these values for a and b in the general formula gives:
$$area=225=\frac{1}{2}(h+3+h+7)h=h ^{2}+5h$$

kropot72 · Answer

So you need to solve the following quadratic:
$$h ^{2}+5h-225=0$$

kropot72 · Answer

@k.rene.s Do you know how to solve the quadratic?

anonymous · Answer

@kropot72 yes now that you put it in that formula I was able to solve THANKS!

kropot72 · Answer

You're welcome :)

anonymous · Answer

The area of a trapezoid is A = (1/2) * (b1 + b2) * h
A = (1/2) * ((h + 3) + (h + 7)) * h
A = (1/2) * (2h + 10) * h

***


A = (h + 5) * h
A = h^2 + 5h
h^2 + 5h = 225
h^2 + 5h - 225 = 0

h = (-5 +/- sqrt(5^2 - 4 * 1 * -225)) / (2 * 1)
h = (-5 +/- sqrt(25 + 900)) / 2
h = (-5 +/- sqrt(925)) / 2
h = (-5 +/- sqrt(925)) / 2

h has two solutions, about -17.71 and about 12.71.Since real life has no negative numbers, the height is 12.71 yards and the two bases are 15.71 and 22.71 yards.

2.   A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. She wants the area to be 225 square yards. The situation is modeled by the equation, , where h is the height, in yards, and b1 and b2 are the length of the two bases, in yards. Complete the square to find the height that will give the desired area. Round to the nearest hundredth of a yard. 

 (1 point)
  (0 pts) 25.41 yards
  (0 pts) 460 yards
  (0 pts) 15.21 yards
  (1 pt) 12.71 yards
1 /1 point