Answer:
The dimensions of the table are [tex]6 ft \times 2 ft[/tex]
Step-by-step explanation:
Let x be the length of table
Let y be the breadth of table
Area of table = [tex]Length \times Breadth = xy[/tex]
We are given that Table has an area of 12 sq.feet
xy=12
[tex]y =\frac{12}{x}[/tex] -----1
Perimeter of table = 2(l+b)=2(x+y)
We are given that Perimeter is 16 feet
2(x+y)=16
x+y=8
Using 1
[tex]x+\frac{12}{x}=8\\\frac{x^2+12}{x}=8\\x^2-8x+12=0\\x^2-6x-2x+12\\x(x-6)-2(x-6)=0\\(x-6)(x-2)=0\\x=6,2[/tex]
When x = 6
y = [tex]\frac{12}{6}=2[/tex]
When x = 2
y = [tex]\frac{12}{2}=6[/tex]
Hence the dimensions of the table are [tex]6 ft \times 2 ft[/tex]
