Question

Table has an area of 12 and a perimeter of 16 feet what are the dimensions of the table

Answer 1

The dimensions of the table are
`6 ft * 2 ft`

Explanation:

Let x be the length of table

Let y be the breadth of table

Area of table =
`Length * Breadth = xy`

We are given that Table has an area of 12 sq.feet

xy=12

`y =(12)/(x)` -----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

`x+(12)/(x)=8\\(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`

When x = 6

y =
`(12)/(6)=2`

When x = 2

y =
`(12)/(2)=6`

Hence the dimensions of the table are
`6 ft * 2 ft`