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

Answer:

Length = 7 cm

Width = 2 cm

Step-by-step 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:

$l = 2\times w +3 ....... (1)$

Formula for perimeter of a rectangle is given as:

$P = 2 \times (Length + Width)$

OR

$P = 2 \times (l + w)$

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

$18 = 2 \times (2w +3 + w)\\\Rightarrow \dfrac{18}2 = 3w +3 \\\Rightarrow 9 = 3w +3\\\Rightarrow 3w = 9 -3\\\Rightarrow w = \dfrac{6}{3}\\\Rightarrow w = 2\ cm$

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

$l = 2\times 2 +3 \\\Rightarrow l = 4+3\\\Rightarrow l = 7\ cm$

So, the dimensions are:

Length = 7 cm

Width = 2 cm