A rectangular garden is 2m longer than its width...

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KJBlue

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Hi all wanted to clarify if I have done this right or if I'm wrong?

Question:
1. A rectangular garden is 2m longer than its width.
a) Write an expression for the area of the garden with brackets.
b) If the width of the garden is 6 m, find its length and its area

My process,
According to the given information the length of the rectangle is equal to ’x+2’ and width is ‘x’
Length = x + 2
width = x

(a) Area of a rectangle is,
A = l x w
= (x + 2) x x
= x(x + 2)
= x2 + 2x

(b) Insert w = 6 into the equation,
A = l x w
= (x + 2) x 6
= 6(x + 2)
= 6x + 12

Is this correct? I'm not 100% sure and want to check, THANK YOU! :)
 
First, never use "x" to mean multiplication in algebra, especially when what you're multiplying is the variable x!

For (a), they don't want your final answer, which doesn't have brackets. They just want x(x + 2).

For (b), you need to use your result from (a). Do you see that x = w = 6? There should be no x in the answer, because you have a number for it. Just plug in x = 6 into x(x + 2). You also didn't say what the length is, as requested.
 
There is never a reason why you should know the value for some x's and not for other xs. If that is truly the case then you did not define x carefully. If you conclude that x=6 then you have no way out of that fact. Any and all x's equal 6. This of course is just what Dr Peterson stated.
 
Thank you both, appreciate it!

For length since x = w = 6, then length being (x + 2),
length = 6 + 2
= 8
 
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