Answer:
60 square foot
Step-by-step explanation:
Perimeter of a rectangular garden = 58 foot
Let x and y denote length and width of the rectangular garden.
2 (Length + Width) = Perimeter of the rectangular garden
[tex]2(x+y)=58\\x+y=\frac{58}{2}\\ x+y=29[/tex]
So,
length = x
width = y = [tex]29-x[/tex]
The length is reduced by 7 feet and the width becomes half.
New length = [tex]x-7[/tex]
New width = [tex]\frac{1}{2}(29-x)[/tex]
New perimeter = 34 foot
[tex]2[(x-7)+\frac{1}{2}(29-x)]=34\\ 2[2(x-7)+(29-x)]=2(34)\\2(x-7)+(29-x)=34\\2x-14+29-x=34\\2x-x-14+29=34\\x+15=34\\x=34-15\\x=19[/tex]
So,
New length [tex]=x-7=19-7=12\,\,foot[/tex]
New width = [tex]\frac{1}{2}(29-19)=\frac{1}{2}(10)=5\,\,foot[/tex]
Area of the new smaller garden = New length × New Width
= 12 × 5
= 60 square foot
