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 295 square yards. The situation is modeled by the equation h2 + 5h = 295. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard.
can someone help me please
so, what is confusing about using the quadratic formula?
h^2 + 5h - 295 = 0
h = (-5±√(5^2 + 4*295)]/2
not so bad, eh?
To find the height that will give the desired area, we need to solve the quadratic equation h^2 + 5h = 295 using the quadratic formula.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 5, and c = -295. Plugging these values into the formula, we get:
h = (-5 ± √(5^2 - 4(1)(-295))) / (2(1))
Simplifying inside the square root:
h = (-5 ± √(25 + 1180)) / 2
h = (-5 ± √(1205)) / 2
The square root of 1205 is approximately 34.71.
h = (-5 ± 34.71) / 2
To find the two possible values of h, we use both the plus and minus signs:
h1 = (-5 + 34.71) / 2 ≈ 14.86
h2 = (-5 - 34.71) / 2 ≈ -19.86
Since height cannot be negative, we disregard h2.
Therefore, the height that will give the desired area is approximately 14.86 yards (rounded to the nearest hundredth).
To find the height that will give the desired area, we can start by rearranging the equation h^2 + 5h = 295 to the standard quadratic form ax^2 + bx + c = 0.
In this case, a = 1, b = 5, and c = -295.
Now, we can use the Quadratic Formula, which states that for a quadratic equation ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In our case, substituting the values of a, b, and c, we get:
h = (-5 ± √(5^2 - 4(1)(-295))) / (2(1))
Simplifying further:
h = (-5 ± √(25 + 1180)) / 2
h = (-5 ± √(1205)) / 2
Now we can find the two possible heights:
h1 = (-5 + √(1205)) / 2
h2 = (-5 - √(1205)) / 2
Using a calculator, we can evaluate these expressions and round to the nearest hundredth of a yard.
h1 ≈ 14.34 yards
h2 ≈ -19.34 yards
Since height cannot be negative, we can ignore the negative value.
Therefore, the height that will give the desired area is approximately 14.34 yards (rounded to the nearest hundredth of a yard).