Question

Ok guy's... There is one more question after this one that I need help with, so if you guys could help me out with these 2 questions I have left That would be great! And then I can get out of your hair! :)
A rectangle has an area of 12 square centimeters and a perimeter of 16 centimeters. Which of the following could be its dimensions?

Answer 1

\[A_\text{rectangle}=b\times h\]
\[P_\text{rectangle}=b+h+b+h=2(b+h)\]

Answer 2

what are your options?

Answer 3

\[bh=12\qquad\qquad(i)\]\[2(b+h)=16\qquad(ii)\]
\[b+h=8\qquad\qquad(ii)/2\]\[b=8-h\qquad\qquad(iii)\]

\[(8-h)h=12\qquad(iii)\to(i)\]
\[8h-h^2=12\]\[0=h^2-8h+12\]\[0=(h-2)(h-6)\]

Answer 4

These are my choices! :)
A. 2 cm and 6 cm
B. 3 cm and 4 cm
C. 1.5 cm and 8 cm
D. 1 cm and 12 cm

Answer 5

the correct dimensions will solve both of these equations simultaneously,
\[bh=12\],\[2(b+h)=16\]

ie the dimensions will multiply to give twelve, and add to give 8