Question

A rectangular carpet has a perimeter of 244 inches. The length of the carpet is 90 inches more than the width. Determine the dimensions of the carpet by solving the equation 2w+2(w+90)=244​, where w represents the carpet width.

Answer 1

The dimensions of rectangle are:

Width = 16 inches

Length = 106 inches

Explanation:

Perimeter of rectangle = 244 inches

Let Width of rectangle = w

Length of rectangle = w+90

We need to find the dimensions (length and width) of the carpet

The formula used will be:
`Perimeter=2(length+width)`

Putting values and making equation:

`244=2w+2(w+90)\\Solving:\\244=2w+2w+180\\244=4w+180\\Switching\:sides\\4w+180=244\\Subtracting\:180\:from\:both\:sides\\4w=244-180\\4w=64\\Dividing\:both\:sides\:by\:4\\(4w)/(4) =(64)/(4)\\w=16`

So, we get w = 16

The width w = 16 inches

Now, finding length = w+ 90 = 16+90 = 106 inches

Therefore the dimensions of rectangle are:

Width = 16 inches

Length = 106 inches