Question 1206410
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L = length
W = width
2(L+W) = perimeter = 74
2(L+W) = 74
L+W = 74/2
L+W = 37
L = 37-W


L*W = area
(37-W)*W = 330
-W^2 + 37W - 330 = 0
W^2 - 37W + 330 = 0


Apply the quadratic formula (when a = 1, b = -37, c = 330)
{{{W = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{W = (-(-37)+-sqrt((-37)^2-4(1)(330)))/(2(1))}}}


{{{W = (37+-sqrt(1369 - 1320))/(2)}}}


{{{W = (37+-sqrt(49))/(2)}}}


{{{W = (37+-  7)/(2)}}}


{{{W = (37+7)/(2)}}} or {{{W = (37-7)/(2)}}}


{{{W = (44)/(2)}}} or  {{{W = (30)/(2)}}}


{{{W = 22}}} or  {{{W = 15}}}



If W = 22, then L = 37-W = 37-22 = 15
And vice versa if W = 15 then it leads to L = 22.
The order of L and W doesn't matter.


Check:
perimeter = 2*(L+W) = 2*(22+15) = 74
area = L*W = 22*15 = 330
Everything is confirmed.


Answer: <font color=red>22 inches by 15 inches</font>
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