A rectangle has sides of 3x+5 and 5x-2. Give the polynomial that represents its perimeter.
16x+6.
Process:
2(3x+5) + 2(5x-2) = 6x + 10 + 10x - 4 = 16x+6
To find the perimeter of a rectangle, you need to add the lengths of all four sides. In this case, the rectangle has sides of 3x+5 and 5x-2.
The perimeter of a rectangle is given by the formula: P = 2 (length + width)
So, the perimeter of this rectangle can be calculated as follows:
P = 2(3x+5 + 5x-2)
To simplify the expression, you need to distribute the 2 to both terms inside the parentheses:
P = 2(3x + 5) + 2(5x - 2)
Next, you can use the distributive property to simplify each term:
P = 6x + 10 + 10x - 4
Combining like terms:
P = (6x + 10x) + (10 - 4)
P = 16x + 6
Therefore, the polynomial that represents the perimeter of the rectangle is 16x + 6.