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

User Yshavit
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1 Answer

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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.

User Sven Borden
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