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 linger base to be 7 yards greater than the height. She wants the area to be 295 square yards. The situation is molded by the equation h^2+5h=295. Use quadratic formula to find the height that will give the desired area. Round to the nearest hundredth of a yard.
Could someone please explain.
I got 14.86 yards not sure if right
14.86 years is THE CORRECT ANSWER i took the test.
To find the height that will give the desired area of a trapezoid-shaped flower garden, you can use the given equation: h^2 + 5h = 295.
To solve this quadratic equation, you can rearrange it into a standard form: h^2 + 5h - 295 = 0.
Now, you can use the quadratic formula, which states that for the quadratic equation ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 5, and c = -295. Plugging these values into the quadratic formula, we get:
h = (-5 ± √(5^2 - 4(1)(-295))) / (2(1))
Simplifying the equation:
h = (-5 ± √(25 + 1180)) / 2
h = (-5 ± √1205) / 2
To find the approximate values of h, we need to calculate the square root of 1205, which is approximately equal to 34.71.
So, substituting this value:
h = (-5 ± 34.71) / 2
Therefore, we have two possible solutions:
1. h = (-5 + 34.71) / 2 ≈ 29.71 / 2 ≈ 14.86
2. h = (-5 - 34.71) / 2 ≈ -39.71 / 2 ≈ -19.86
Since height cannot be negative, we discard the second solution.
Therefore, the height that will give the desired area, rounded to the nearest hundredth of a yard, is approximately 14.86 yards.
To solve the equation h^2 + 5h = 295 for the height h, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation h^2 + 5h = 295, a = 1 (the coefficient of h^2), b = 5 (the coefficient of h), and c = -295. Applying these values to the quadratic formula, 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 calculate the two possible solutions for h:
h1 = (-5 + √(1205)) / 2
h2 = (-5 - √(1205)) / 2
Rounding these values to the nearest hundredth of a yard, we can determine the height that will give the desired area.