Question

Find the area and perimeter of the following rectangle. The lengths are 4x+y+2; and 3x+3y. The widths are 2x+y+1 and 12

Answer 1

Equating the lengths, we have:
`4x+y+2=3x+3y\Rightarrow x-2y=-2`

Equating the widths, we have:
`2x+y+1=12\Rightarrow2x+y=11`

Solving the two equations simultaneously gives that x = 4 and y = 3.

Thus, the length is 4(4) + 3 + 2 = 21 and the width is 12.

Therefore area = length times width = 21 x 12 = 252 square units

perimeter = 2(length + width) = 2(21 + 12) = 2(33) = 66.