Mathematics: Ms. Ahmed has a rectangular garden where she grows tomatoes. The length of her garden is represented by t + 4 and the width by 2t - 1. Express the area of Ms. Ahmed s garden as a polynomial in standard form. If the area of Ms. Ahmed s garden is 56 ft2, what are the dimensions of the garden?

Ms. Ahmed has a rectangular garden where she grows

shelovejaylocs

28.01.2022

The dimension is 8ft by 7ft

Step-by-step explanation:

Given data

Length l = (t+4)

Width w= (2t-1)

the area is expressed as A= length * width

$A= (t+4)*(2t-1)\\A= t(2t-1) +4(2t-1)\\A= 2t^{2}-t+8t-4\\$

collecting like terms we have

$A= 2t^{2} +7t-4$

hence our expression for area is $A= 2t^{2} +7t-4$

given that the area is $56ft^{2}$ to solve for the sides we need to first solve fot t

equating the expression for area to 56 we can solve for t

$A= 2t^{2} +7t-4= 56$

taking the constant term to the other side and solve we have

$A= 2t^{2} +7t-4-56\\A= 2t^{2} +7t-60\\$

we can substitute two factors for 7t that when multiplied we give -60 and when added we give 7 these factors are 15 and -8

$A= 2t^{2} +7t-60\\\\A= 2t^{2} -8t+15t-60\\2t^{2} -8t+15t-60=0\\\\2t(t-4) +15(t-4)= 0\\2t+15=0, (t-4)= 0\\2t=-15, t= -7.5\\t= 4$

t=4 hence the length is

$(t+4)\\(4+4)= 8ft\\$

hence the width is

$(2t-1)\\(2*4-1)= (8-1)= 7ft$

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