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
