Alandscaper 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 yards b: 600 yards c: 14.86 yards d: 29.71 yards

The height is 14.86 yards ⇒ answer C

Step-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 ,

  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

∴

∴

∴

- OR

∴

- 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

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step-by-step explanation: