The area of a rectangle is 72cm square. length,/, of the rectangle is 6 cm longer than the width w

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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