[size=150]A rectangle with dimensions 6 cm and [math]w[/math] cm is partitioned into two smaller rectangles.[br][img]data:image/png;base64,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[/img][br][br]Explain why each of these expressions represents the area, in cm[sup]2[/sup], of the shaded region.[/size][br][br][math]6w-24[/math]

[math]6(w-4)[/math]

[size=150][size=100]Suppose that [math]x[/math] is 3. Find the area of each square in the diagram. Then find the area of the large rectangle.[/size][/size]

Find the side lengths of the large rectangle assuming that [math]x[/math] is 3. Find the area of the large rectangle by multiplying the length times the width. Check that this is the same area you found before.

Now suppose that we do not know the value of [math]x[/math]. Write an expression for the side lengths of the large rectangle that involves [math]x[/math].