Question

1. find the perimeter of the rectangle:

$3x^2 + 6x - 10$
$3x + 5$

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Let length \( l = 3x^2 + 6x - 10 \) and width \( w = 3x + 5 \).

Step2: Substitute into formula

\( P = 2\times[(3x^2 + 6x - 10)+(3x + 5)] \)

Step3: Simplify inside the brackets

Combine like terms: \( (3x^2 + 6x - 10)+(3x + 5)=3x^2+(6x + 3x)+(-10 + 5)=3x^2 + 9x - 5 \)

Step4: Multiply by 2

\( P = 2\times(3x^2 + 9x - 5)=6x^2 + 18x - 10 \)

Answer:

\( 6x^2 + 18x - 10 \)