Question 1153532
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The answer is <font color=red>6 feet</font>


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How to get this answer:


h = height
b1 = longer base = 18 ft
b2 = shorter base = h
A = area of trapezoid = 72 square ft


{{{A = (h*(b1+b2))/2}}} area of trapezoid formula


{{{72 = (h*(18+h))/2}}} plug in given values


{{{72*2 = h*(18+h)}}} Multiply both sides by 2


{{{144 = 18h+h^2}}} Distribute


{{{0 = 18h+h^2-144}}} Subtract 144 from both sides


{{{0 = h^2+18h-144}}}


{{{h^2+18h-144 = 0}}} Get equation into standard form


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Use the quadratic formula to solve for h
We will plug in: a = 1, b = 18, c = -144


{{{h = (-b+sqrt(b^2-4ac))/(2a)}}} or {{{h = (-b-sqrt(b^2-4ac))/(2a)}}}


{{{h = (-18+sqrt((18)^2-4(1)(-144)))/(2(1))}}} or {{{h = (-18-sqrt((18)^2-4(1)(-144)))/(2(1))}}}


{{{h = (-18+sqrt(900))/(2)}}} or {{{h = (-18-sqrt(900))/(2)}}}


{{{h = (-18+30)/(2)}}} or {{{h = (-18-30)/(2)}}}


{{{h = (12)/(2)}}} or {{{h = (-48)/(2)}}}


{{{h = 6}}} or {{{h = -24}}}


Ignore the negative solution for h. A negative height does not make sense.


The only possible height value is h = 6.
Therefore, the shorter base is also 6 ft long.


Let's check to see if b1 = 18, b2 = 6, and h = 6 all lead to an area of 72
{{{A = (h*(b1+b2))/2}}}


{{{A = (6*(18+6))/2}}}


{{{A = (6*24)/2}}}


{{{A = 144/2}}}


{{{A = 72}}}


The answer is confirmed.

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