a landscaper is designing a flower garden in the shape of a trapezoid. she want to make to shorter base 3 yards greater than the height and the longer base 7 yards greater than the base. she wants the area 295 square yards. the situation is modeled by the equation h^2+5h=295. use the quadratic formula to find the height that will give the desired area
To solve the quadratic equation h^2 + 5h = 295, we can rearrange the equation to bring all terms to one side:
h^2 + 5h - 295 = 0
The quadratic formula is given by:
h = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the coefficients are:
a = 1
b = 5
c = -295
Plugging these values into the quadratic formula, we have:
h = (-5 ± √(5^2 - 4(1)(-295))) / (2(1))
h = (-5 ± √(25 + 1180)) / 2
h = (-5 ± √1205) / 2
Therefore, the two possible values for the height that will give the desired area are:
h ≈ 12.16 yards or h ≈ -17.16 yards
Since the height cannot be negative in this context, the height of the flower garden is approximately 12.16 yards.