Respuesta :
Given:
The length of the given rectangle is l =(2x+2) cm.
The width of the given rectangle is w =(3x-3) cm.
The perimeter of the given rectangle is P =58cm.
Required:
We need to find the area of the rectangle.
Explanation:
Consider the perimeter of the rectangle formula.
[tex]P=2(l+w)[/tex]Substitute l=2x+2, w =3x-3 and P=58 in the formula.
[tex]58=2(2x+2+3x-3)[/tex][tex]58=2(5x-1)[/tex][tex]58=10x-2[/tex]Add 2 to both sides of the equation.
[tex]58+2=10x-2+2[/tex][tex]60=10x[/tex]Divide both sides by 10.
[tex]\frac{60}{10}=\frac{10x}{10}[/tex][tex]x=6[/tex]Substitute x =6 in the equations l=2x+2.
[tex]l=2x+2=2(6)+2=12+2=14cm[/tex][tex]Substitute\text{ }x=6\text{ }in\text{ }the\text{ }equations\text{ }w=3x-3.[/tex][tex]w=3x-3=3(6)-3=18-3=15cm[/tex]The area of the rectangle is
[tex]A=lw[/tex]Substitute l=14cm and w =15cm in the formula.
[tex]A=14\times15[/tex][tex]A=210cm^2[/tex]Final answer:
The area of the given rectangle is 210 square cm.
