Answer:
The lengths of the sides of the rectangle are 13 inches and 15 inches
Step-by-step explanation:
The perimeter of a rectangle
Given the two sides of a rectangle a and b. The perimeter of the rectangle is:
[tex]P=2(a+b)[/tex]
We are given the perimeter of a rectangle as:
[tex]P=8(2x+1)[/tex]
And each side has a length of 3x+4 and 4x+3. Calculating the perimeter:
[tex]P=2(3x+4+4x+3)=2(7x+7)[/tex]
We set up the equation:
[tex]8(2x+1)=2(7x+7)[/tex]
Dividing by 2:
[tex]4(2x+1)=7x+7[/tex]
Operating:
[tex]8x+4=7x+7[/tex]
Subtracting 7x:
[tex]x+4=7[/tex]
Subtracting 4:
x=3
The length of each side is:
3x+4=3*3+4=13
4x+3=4*3+3=15
The lengths of the sides of the rectangle are 13 inches and 15 inches
