Question

3 select the correct answer. the length of a rectangle is 3 meters more than the width. the perimeter of the rectangle is 26 meters. if the width is b, which equation represents the situation? how many solutions will this equation have? a. (b + 3)(b) = 26, which has one solution b. 2(b + 3) + 2b = 26, which has infinitely many solutions c. 2(b + 3) + b = 26, which has one solution d. 2(b + 3) + b = 26, which has no solution

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The perimeter formula of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Given that the length \(l=b + 3\) (since the length is 3 meters more than the width \(b\)) and \(P = 26\).
Substitute \(l=b + 3\) and \(w = b\) into the perimeter formula: \(2[(b + 3)+b]=26\).

Step2: Simplify the equation

First, simplify the expression inside the brackets: \((b + 3)+b=2b + 3\). Then the equation becomes \(2(2b + 3)=26\).
Divide both sides of the equation by 2: \(2b+3 = 13\).
Subtract 3 from both sides: \(2b=10\).
Divide both sides by 2: \(b = 5\). A linear equation in one variable \(ax + b=0\) (\(a
eq0\)) has exactly one solution.

Answer:

C. \(2[(b + 3)+b]=26\), which has one solution