Question

one side of a rectangle is 12 and the perimeter is 34. what is the area?

Answer 1

60

Answer 2

You know the formulas for perimeter and area:\[A=lw\]and\[P=2l+2w\]where l is the length and w the width. You know that one of the dimensions, l or w (it doesn't matter) is 12. You're also given the perimeter, so you can use this information to obtain the other dimension, and therefore, your area.

Let's say l=12. Then\[P=34=2w+2(12)=2w+24 \rightarrow w=\frac{34-24}{2}=5\]Therefore, the area is\[A=lw=12 \times 5 = 60\] square units.