Question

A rectangle with perimeter 18 cm has a length that is 3 cm more than twice its width. Find the dimensions of the rectangle. SOLVE EACH APPLICATION USING ALGEBRA. TYPE THE EQUATION OR INEQUALITY AND PLEASE SHOW WORK.

Answer 1

Length = 7 cm

Width = 2 cm

Explanation:

Perimeter of rectangle = 18 cm

Let length of rectangle =
`l` cm

Let width of rectangle =
`w` cm

As per given statement, length is 3 cm more than the twice of its width:

Writing equation:

`l = 2* w +3 ....... (1)`

Formula for perimeter of a rectangle is given as:

`P = 2 * (Length + Width)`

OR

`P = 2 * (l + w)`

Putting values of P as given and
`l` by using equation (1):

`18 = 2 * (2w +3 + w)\\\Rightarrow \frac{18}2 = 3w +3 \\\Rightarrow 9 = 3w +3\\\Rightarrow 3w = 9 -3\\\Rightarrow w = (6)/(3)\\\Rightarrow w = 2\ cm`

Putting value of
`w` in equation (1):

`l = 2* 2 +3 \\\Rightarrow l = 4+3\\\Rightarrow l = 7\ cm`

So, the dimensions are:

Length = 7 cm

Width = 2 cm