## The perimeter of a rectangle is 54 cm. Find its length and width if the length is represented by 3x + 2 and the width is represented b

Question

The perimeter of a rectangle is 54 cm. Find its length and width if the length is represented
by 3x + 2 and the width is represented by 2x – 5.

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2 months 2021-09-02T05:24:41+00:00 2 Answers 1 views 0

Length = 20 cm

Width = 7 cm

Step-by-step explanation:

Given that :

• The perimeter of a rectangle is 54 cm.
• Its length and width if the length is represented by 3x + 2 and the width is represented by 2x – 5.

To find :-

Find the measures of length and width

Solution :-

• To calculate the measures of length and width of rectangle . we gave given in question that perimeter of rectangle is 54 cm and length is represented by 3x + 2 and width is represented by 2x-5.

Using Formula :-

Perimeter of rectangle = 2 ( l + b )

Where,

• l is the length and w is the width of rectangle.
• Perimeter = 54 cm

Substitute the values

54 cm = 2 ( 3x + 2 + 2x – 5 )

Combine like terms

54 cm = 2 ( 3 x + 2 x + 2 – 5)

54 cm = 2 ( 5 x -3)

Simplify both sides of the equation.

54 = 2( 5x− 3 )

54 = (2)(5x) + (2)(−3). .. ( Distribute )

54 = 10x +−6

54 = 10x −6

Flip the equation.

10x −6 = 54

10x −6 + 6 = 54 + 6

10x = 60

Divide both sides by 10.

10x / 10 = 60 / 10

x = 6

Therefore ,

Length = 3x + 2 =3 ×6 + 2 = 18 + 2 = 20 cm

Width = 2x- 5 = 2 × 6 – 5 = 12 – 5 = 7 cm

length = 20

width = 7

Step-by-step explanation:

Perimeter of a rectangle is

P = 2(l+w)

54 = 2( 3x+2 + 2x-5)

Combine like terms

54 = 2( 5x -3)

Divide each side by 2

54/2 = 5x-3

27 = 5x-3

27+3 = 5x-3+3

30 = 5x

Divide by 5

30/5 = 5x/5

6 =x

3x+2 = 3(6)+2 = 18+2 = 20

2x-5 = 2(6)-2 =12-5 =7