Answer
We can represent the perimeter of the rectangle by 8x + 6.
Work Step by Step
The formula for the perimeter of a rectangle is 2a + 2b, where a and b are the rectangle's length and width.
By looking at the figure, we can see that:
a = 3x + 5
b = x - 2
So, we substitute these values into the formula to obtain:
Perimeter of the rectangle = 2 $\times$ (3x + 5) + 2 $\times$ (x - 2)
Use the distributive property.
Perimeter of the rectangle = 6x + 10 + 2x - 4
Group similar terms.
Perimeter of the rectangle = (6x + 2x) + (10 - 4)
Simplify.
Perimeter of the rectangle = 8x + 6
We can represent the perimeter of the rectangle by 8x + 6.
