Question

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

A) 2 ft by 6 ft
B) 2 ft by 8 ft
C) 4 ft by 3 ft
D) 4 ft by 4 ft

Answer 1

A, 2 ft by 6 ft

Explanation:

Answer 2

p=2x+2y, y=(p-2x)/2

a=xy, using y found above in this equation gives you:

a=(px-2x^2)/2 we are told a=12 and p=16 so

12=(16x-2x^2)/2

24=16x-2x^2

2x^2-16x+24=0

2x^2-12x-4x+24=0

2x(x-6)-4(x-6)=0

(2x-4)(x-6)=0

2(x-2)(x-6)=0

So the table is 2 ft by 6 ft.