An architect plans to build an extension to Meiling's rectangular deck. Let x represent the increase, in meters, of her deck's length. The expression 4(x + 8) represents the area of the deck, where 4 is the width, in meters, and (x+ 8) represents the extended length, in meters. Use the Distributive Property to write an expression that represents the total area of Meiling's new deck.
To find the total area of Meiling's new deck, we need to add the area of the original deck with the area of the extension.
The original deck: Length = x, Width = 4, so the area is 4x.
The extension: Length = x + 8 (since x is the increase in length), Width = 4, so the area is 4(x + 8).
Using the Distributive Property, the expression that represents the total area of Meiling's new deck is:
Total area = 4x + 4(x + 8)
Simplifying this expression gives:
Total area = 4x + 4x + 32
Total area = 8x + 32