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.

Step-by-step 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.

`(60)/(10)=(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*15`
`A=210cm^2`

Final answer:

The area of the given rectangle is 210 square cm.