Question

The perimeter of a rectangle measuring (2x + 2)cm by (3x -3) cm is 58cm. Calculate its area. 13. The perimeter

Answer 1

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.

$P=2(l+w)$

Substitute l=2x+2, w =3x-3 and P=58 in the formula.

$58=2(2x+2+3x-3)$$58=2(5x-1)$$58=10x-2$

Add 2 to both sides of the equation.

$58+2=10x-2+2$$60=10x$

Divide both sides by 10.

$\frac{60}{10}=\frac{10x}{10}$$x=6$

Substitute x =6 in the equations l=2x+2.

$l=2x+2=2(6)+2=12+2=14cm$$Substitute\text{ }x=6\text{ }in\text{ }the\text{ }equations\text{ }w=3x-3.$$w=3x-3=3(6)-3=18-3=15cm$

The area of the rectangle is

$A=lw$

Substitute l=14cm and w =15cm in the formula.

$A=14\times15$$A=210cm^2$

Final answer:

The area of the given rectangle is 210 square cm.