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TOLLYOISTHIS2774
19.06.2021 •
Mathematics
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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Ответ:
length = 20
width = 10
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
Add 3 to each side
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 =12-2 =10
Ответ:
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 cmSubstitute 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
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