Answer:
Area of the garden in standard form:
Area = (2t^2) + 7t - 4
The dimension of the garden is 8ft × 7ft
Step-by-step explanation:
Length of the rectangular garden, L = t+4
Width of the garden, B = 2t - 1
Area = length * width
Area = (t+4) * ( 2t-1)
Area = (2t^2) + 7t - 4..….......(1)
If the Area = 56 ft^2
Substitute Area into (1)
56 = (2t^2) + 7t - 4
(2t^2) + 7t - 60 = 0
(2t^2) - 8t + 15t - 60 = 0
2t(t - 4) + 15(t - 4) = 0
(2t+15) (t-4) = 0
Let 2t + 15 =0
t = -7.5
Let t - 4 = 0
t = 4
* When t = -7.5
Length, L = -7.5 + 4 = -3.5 ft
Width, B = 2(-7.5) -1 = -16 ft
Since length and breadth cannot be negative, t = -7.5 is not possible
** When t = 4
Length, L = 4+4 = 8 ft
Width, B = 2(4) - 1 = 7 ft
Therefore, the dimension of the garden is 8ft × 7ft
Answer:
The dimension is 8ft by 7ft
Step-by-step explanation:
Given data
Length l = [tex](t+4)[/tex]
Width w= [tex](2t-1)[/tex]
the area is expressed as [tex]A= length * width[/tex]
[tex]A= (t+4)*(2t-1)\\A= t(2t-1) +4(2t-1)\\A= 2t^{2}-t+8t-4\\[/tex]
collecting like terms we have
[tex]A= 2t^{2} +7t-4[/tex]
hence our expression for area is [tex]A= 2t^{2} +7t-4[/tex]
given that the area is [tex]56ft^{2}[/tex] to solve for the sides we need to first solve fot t
equating the expression for area to 56 we can solve for t
[tex]A= 2t^{2} +7t-4= 56[/tex]
taking the constant term to the other side and solve we have
[tex]A= 2t^{2} +7t-4-56\\A= 2t^{2} +7t-60\\[/tex]
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
[tex]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[/tex]
t=4 hence the length is
[tex](t+4)\\(4+4)= 8ft\\[/tex]
hence the width is
[tex](2t-1)\\(2*4-1)= (8-1)= 7ft[/tex]
