SOLUTION: 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 th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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 th      Log On


   

Question 1021644: 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 245 square yards. The situation is modeled by the equation h%5E2%2B5h=245. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
If the equation is correct, just solve for h. Maybe general form is factorable or maybe not.

The bases are lengths h+3 and h+7; so the average is %28h%2B3%2Bh%2B7%29%2F2=%282h%2B10%29%2F2=h%2B5, and the trapezoid area will be %28h%2B5%29%2Ah=245, since the area is given.

As already stated, either h%5E2%2B5h-245=0 is or is not factorable. Since you are told use quadratic formula, ...
h=%28-5%2B-+sqrt%285%5E2-4%2A%28-245%29%29%29%2F2
Simplify and choose what value makes sense.