Given:
The perimeter of a rectangle is 84cm.
The length is 12 cm longer than the width.
Required:
We need to find the length and width of the rectangle.
Explanation:
Let l be the length of the rectangle and w be the width of the rectangle.
The length is 12 cm longer than the width.
Add 12 to the width to get the length.
[tex]l=12+w[/tex]Consider the perimeter of the rectangle formula.
[tex]P=2(l+w)[/tex]Substitute l=12+w and P =84 in the formula.
[tex]84=2(12+w+w)[/tex][tex]84=24+4w[/tex]Subtract 24 from both sides of the equation.
[tex]84-24=4w[/tex][tex]60=4w[/tex]Divide both sides of the equation by 4.
[tex]15=w[/tex]Substitute w =15 in the equation l=12+w.
[tex]l=12+15[/tex][tex]l=27[/tex]Final answer:
The length of the rectangle is 27 cm.
The width of the rectangle is 15 cm.
