Question

the length of a rectangle in terms of ( x ) is ( 5x^{2}+3x + 6 ) and its width is ( 7x + 9 ), what is the perimeter of this rectangle?
( x^{2}+12x + 15 )
( 10x^{2}+20x + 30 )
( 20x^{2}+20x + 30 )
( 20x^{2}+20x + 30 )

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The formula for the perimeter \(P\) of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width.

Step2: Substitute the given expressions for length and width into the formula

Given \(l=5x + 3\) and \(w = 7x+9\). Then \(P=2((5x + 3)+(7x + 9))\).

Step3: Simplify the expression inside the parentheses

First, combine like - terms inside the parentheses: \((5x+3)+(7x + 9)=5x+7x+3 + 9=12x+12\).

Step4: Multiply by 2

Now, \(P = 2(12x + 12)\). Using the distributive property \(a(b + c)=ab+ac\), we get \(P=2\times12x+2\times12 = 24x+24\).

Answer:

\(24x + 24\)