MATH SOLVE

2 months ago

Q:
# 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 h^2 + 5h = 295. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard. A: 17.36 yardsB: 600 yardsC: 14.86 yardsD: 29.71 yards

Accepted Solution

A:

Answer:The height is 14.86 yards ⇒ answer CStep-by-step explanation:* Lets explain how to solve the problem- The flower garden in the shape of a trapezoid- The shorter base to be 3 yards greater than the height- The longer base to be 7 yards greater than the height- The area must be 295 square yards- The situation is modeled by the equation h² + 5h = 295- We want to find the height that will give the desired area by using the quadratic formula- The quadratic formula is [tex]h=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex], where a is the coefficient of h² and b is the coefficient of h and c is the numerical term- The equation of the area is h² + 5h = 295 ∵ h² + 5h = 295 - Subtract 295 from both sides∴ h² + 5h - 295 = 0- Lets find the values of a , b and c from the equation∵ a = 1 , b = 5 , c = -295∴ [tex]h=\frac{-5+-\sqrt{(5)^{2}-4(1)(-295)}}{2(1)}[/tex]∴ [tex]h=\frac{-5+-\sqrt{25+1180}}{2}[/tex]∴ [tex]h=\frac{-5+\sqrt{1205}}{2}=14.86[/tex]- OR ∴ [tex]h=\frac{-5-\sqrt{1205}}{2}=-19.86[/tex]- The dimensions of any figure must be positive value, then we will neglect the negative value of h∴ h = 14.86* The height is 14.86 yards