The length of a rectangle is 3x+3 and the width is 2x. the perimeter of the rectangle is 146 units. what is the length of the longer side?

Let's solve this problem step-by-step.

STEP-BY-STEP EXPLANATION:

Let's first visually represent the problem as a diagram so that we can better understand it. The diagram is attached above.

Next we will establish the following to solve for ( x ).

Perimeter of a rectangle = Sum of the length of all 4 sides of the rectangle

146 = 2 ( 3x + 3 ) + 2 ( 2x )

146 = 6x + 6 + 4x

146 = 10x + 6

10x + 6 = 146

10x = 146 - 6

10x = 140

x = 140 / 10

x = 14

Then we will substitute the value of ( x ) into the expression for the longer side to obtain the value of the length of the longer side.

Longer side of rectangle = 3x + 3

Longer side of rectangle = 3 ( 14 ) + 3

Longer side of rectangle = 42 + 3

Longer side of rectangle = 45

FINAL ANSWER:

Therefore, the length of the longer side of the rectangle is 45 units.

Hope this helps! :)
Have a lovely day! <3

Bis the correct answer