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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

Respuesta :

mrinconj
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
calculista

we know that

The formula to calculate the solutions of the quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex]  is equal to

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

in this problem we have

[tex]h^{2} +5h=295[/tex]

equate to zero

[tex]h^{2} +5h-295=0[/tex]

[tex]a=1\ b=5\ c=-295[/tex]

substitute in the formula

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

[tex]x=\frac{-5(+/-)\sqrt{25+1,180}}{2}[/tex]

[tex]x=\frac{-5(+/-)\sqrt{1,205}}{2}[/tex]

the positive solution is

[tex]x=\frac{-5+\sqrt{1,205}}{2}=14.86\ yd[/tex]

therefore

the answer is

The height is [tex]14.86\ yd[/tex]

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