As you haven't specifically stated what exactly the question is, I will be assuming that the question is most likely asking for what the dimensions ( length and width ) of the rectangle is. With this in mind, I will be answering the question so here I go...
STEP-BY-STEP SOLUTION:
Let's solve this problem step-by-step.
Let's first establish the formula for the area of a rectangle as displayed below:
Area = Length × Width
A = lw
From this, we will establish the values for each of the parts in the area formula using the information given in the problem as displayed below:
A = 72cm^2
l = w + 6
w = w
Now, we will substitute these values into the area formula and then make ( w ) the subject as displayed below:
A = lw
72 = ( w + 6 ) ( w )
72 = w ( w + 6 )
72 = w^2 + 6w
0 = w^2 + 6w - 72
0 = w^2 + 12w - 6w - 72
0 = w ( w + 12 ) - 6 ( w + 12 )
0 = ( w + 12 ) ( w - 6 )
w + 12 = 0
w = 0 - 12
w = - 12
w - 6 = 0
w = 0 + 6
w = 6
As the answer must be positive as measurements are always positive, the answer must be the option which is a positive number.
Therefore:
w = 6
Using the equation we made for the length before, we can substitute the value of ( w ) to obtain the value of the length as displayed below:
l = w + 6
l = ( 6 ) + 6
l = 12
FINAL ANSWER:
The dimensions of the rectangle are:
Length = 12cm
Width = 6cm
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Thank you <3
