How to find the perimeter of a rectangle with fractions

Well, for any rectangle, the perimeter is given by

$$P=2L+2W$$

where $L$ and $W$ are the lengths and widths. Plugging in the values you get, we get

$$P=2\left(\frac5{x+1}\right)+2\left(\frac2x\right)=\frac{10}{x+1}+\frac4x=\frac{14x+4}{x(x+1)}$$

Since the perimeter is given as $20$, then

$$24=\frac{14x+4}{x(x+1)}$$

$$24x(x+1)=14x+4$$

$$24x^2+24x=14x+4$$

$$24x^2+10x-4=0$$

$$12x^2+5x-2=0$$

$$x=\frac{-5\pm11}{20}=\frac14,-\frac23$$

Since $x$ can't be negative, or else we'd have negative side lengths, the correct answer is given as

$$x=\frac14$$

The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. x is in this case the length of the rectangle while y is the width of the rectangle.

The perimeter, P, is:

$$P= x+x+y+y$$

$$P=2x+2y$$

$$P=2(x+y)$$

Example

Find the perimeter of this rectangle:

$$P=7+7+4+4$$

$$P=2\cdot 7+2\cdot 4$$

$$P=2\cdot (7+4)$$

$$P=2\cdot 11$$

$$P=22\,in$$

The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square.

Area, A, is x times y.

$$A=x\cdot y$$

Example

Find the area of this square.

$$A=x\cdot y$$

$$A=5\cdot 5$$

$$A=25\,in^{2}$$

There are different units for perimeter and area The perimeter has the same units as the length of the sides of rectangle or square whereas the area's unit is squared.

Video lesson

Calculate the perimeter and the area in feet