a gardener grows cabbages in her garden that is in the shape of a square. each cabbage takes 1 square feet of area in her garden. this year, she has increased her output by 191 cabbages as compared to last year. the shape of the area used for growing the cabbages has remained a square in both these years. how many cabbages did she produce this year?
Choose the correct choice:
A) 7,251
B) 8406
C) 9216
D) 10,348
E) can not be determined
<gadget id="calculator">191 / 2</gadget>
<output>191/2 = around 95.5</output>

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(191/2) + (1/2)</gadget>
<output>96</output>

<gadget id="calculator">96 ** 2</gadget>
<output>9_216</output>

<result>C</result>
a gardener grows cabbages in her garden that is in the shape of a square. each cabbage takes 1 square feet of area in her garden. this year, she has increased her output by 191 cabbages as compared to last year. the shape of the area used for growing the cabbages has remained a square in both these years. how many cabbages did she produce this year?
power(add(divide(191, const_2), add(const_0_25, const_0_25)), const_2)
"let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 191 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 191 ( x + y ) ( x - y ) = 191 191 is a prime number and thus it will be ( 96 + 95 ) * ( 96 - 95 ) . thus x = 96 and y = 95 x ^ 2 = 96 ^ 2 = 9216 the answer is c ."