Question

a landscaper is designing a flower garden in the shape of a trapezoid. she want to make to shorter base 3 yards greater than the height and the longer base 7 yards greater than the base. she wants the area 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

Answer 1

put you formula in this way: ax^2+bx+c=0 this is h^2+5h-295=0
Now solve with the second grade equation
a=1, b=5, c=-295
you will get h=14.86 and h=-19.86, you can not have negative numbers so the only answer is 14.86

Answer 2

we know that

The formula to calculate the solutions of the quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}}{2a}`

in this problem we have

`h^(2) +5h=295`

equate to zero

`h^(2) +5h-295=0`

`a=1\ b=5\ c=-295`

substitute in the formula

`x=\frac{-5(+/-)\sqrt{5^(2)-4(1)(-295)}}{2*1}`

`x=(-5(+/-)√(25+1,180))/(2)`

`x=(-5(+/-)√(1,205))/(2)`

the positive solution is

`x=(-5+√(1,205))/(2)=14.86\ yd`

therefore

the answer is

The height is
`14.86\ yd`