Question

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[(b + 3) + b] = 26, which has no solution

Answer 1

Answer:  The correct option is

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

Step-by-step explanation:  Given that the length of a rectangle is 3 meters more than its width and the perimeter of the rectangle is 26 meters.

We are to select the correct equation that represents the situation. Also, to find the number of solutions that the equation has if the width is represented by b.

Since the length of the rectangle is 3 meters more then its width, so the length is given by

$l=(b+3)~\textup{meters}.$

Therefore, the perimeter of the rectangle is given by

$2l+2b=P\\\\\Rightarrow 2(b+3)+2b=26\\\\\Rightarrow 2[(b+3)+b]=26~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

And, the solution of equation (i) is given by

$2[(b+3)+b]=26\\\\\Rightarrow 2(2b+3)=26\\\\\Rightarrow 2b+3=\dfrac{26}{2}\\\\\Rightarrow 2b+3=13\\\\\Rightarrow 2b=13-3\\\\\Rightarrow 2b=10\\\\\Rightarrow b=\dfrac{10}{2}\\\\\Rightarrow b=5.$

So, the equation has only one solution.

Thus, the required equation representing the situation is $2[(b+3)+b]=26.$ and the equation has only one solution.

Option (C) is CORRECT.  

Answer 2

I guess B you can move the numbers around but it will still give you the same solution or you could change the sighns