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.

1 answer

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