Question

A table has an area of 12ft squared and a perimeter of 16 ft. What are the dimensions of the table?

2 ft by 6 ft
2 ft by 8 ft
4 ft by 3 ft
4 ft by 4 ft

Answer 1

A) L * W = 12
B) 2L + 2W = 16

A) W = 12 / L then substituting this into B)
B) 2L + 2*12/L = 16
B) 2L + 24 / L = 16 multiplying both sides by "L"
B) 2L^2 +24 = 16L
B) 2L^2 -16L +24 = 0
L = 6
W = 2

Answer 2

Answer: The correct option is (A) 2 ft by 6 ft.

Step-by-step explanation: Given that a table has an area of 12 ft squared and a perimeter of 16 ft.

We are to find the dimensions of the table.

Let l and b denote the length and breadth of the rectangular table, so we have

`Area=12\\\\ \Rightarrow l* b=12\\\\\Rightarrow l=(12)/(b)~~~~~~~~~~~~~~~~(i)`

and

`Perimeter=16\\\\\Rightarrow 2(l+b)=16\\\\\Rightarrow l+b=8\\\\\Rightarrow (12)/(b)+b=8\\\\\Rightarrow b^2-8b+12=0\\\\\Rightarrow b^2-6b-2b+12=0\\\\\Rightarrow (b-2)(b-6)=0\\\\\Rightarrow b-2=0,~~~b-6=0\\\\\Rightarrow b=2,6.`

From equation (i), we get

`l=(12)/(2)=6,\\\\l=(12)/(6)=2.`

Thus, the dimension of the table is 2 ft by 6 ft.

Option (A) is correct.