Answer:
Length = 20 cm
Width = 7 cm
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
Add 6 to both sides.
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