Question

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 yards
B)600 yards
C)14.86 yards
D)29.71 yards
can someone help me?

Answer 1

Well eh..
Area of trapezoid is the (average of bases) * (height)
So, if we mark the height as 'x' we can say:
\[
\frac{(x + 3) + (x + 7)}{2} \cdot x = 295 \\
\frac{2x + 10}{2} \cdot x = 295 \\
(x + 5)x = 295 \\
x^2 + 5x - 295 = 0 \\
x_{1,2} = \frac{ -5 \pm \sqrt{ 25 + 4 \cdot 295 } }{2} \\
x_{1,2} = \frac{ -5 \pm \sqrt{ 1205 } }{2} \\
x_{1,2} = \frac{ -5 \pm 34.71 }{2} \\
x_{1} = \frac{ -5 + 34.71 }{2} = \frac{ 29.71 }{2} = 14.86\\
x_{2} = \frac{ -5 - 34.71 }{2} = - \frac{ 39.71 }{2}
\]
But since x2 is negative.. and height can't be negative, we're left with x1, which is roughly 14.86

Answer 2

Thank you @pitamar