SOLUTION: a park planner has sketched a rectanular park in the first quadrent of a coordinate grid. wo sides of the park lie on the x- and y-axes. a trapezoidal flower bed will be bounded by

Question 120877: a park planner has sketched a rectanular park in the first quadrent of a coordinate grid. wo sides of the park lie on the x- and y-axes. a trapezoidal flower bed will be bounded by the line y=x+7, the x-axis, and the vertical lines x=1 and x=a, where a is greater than 1. The areaA of the trapezoid is modeled by A=1/2a squared+7a-15/2. assume the lengthsamong the axes are measured in meters. For what value of a will the trapezoid have an area of 25 meters? use the quadratic formula to find the answer
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You have an expression in terms of the variable a that represents the area, so all you need to do is set that expression equal to 25 and solve.

Since fractional coefficients will be a pain when you evaluate the quadratic formula, multiply through by 2:

Now add -50 to both sides to get the equation in standard form:

can be excluded because it is clearly less than zero and the problem conditions demand a > 1. So the correct and only answer is:

, roughly 3.7

Should you believe me? Not without checking, you shouldn't.

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