Question

A carpenter built a square table with side length x. Next, he will build a rectangular table by tripling one side and halving the other. The area of the rectangular table is represented by the expression (3 x)(one-half x).
A square with sides x. A rectangle with side one-half x and side 3 x.

What is the simplified expression for the area of the rectangular table?

Three-halves x squared
Three-halves x
Five-halves x squared
Five-halves x

Answer 1

The simplified expression for the area of the rectangular table is Three-halves x squared, 3x²/2

What is the area of the rectangular table?

Since the carpenter built a square table with side length x.  Next, he will build a rectangular table by tripling one side and halving the other.

To find the area of the rectangular table, we know that Area, A = LW where

• L = length and
• W = width

Now, since the length of the square is x, and the rectangular table has one side of the square tripled and halving the other side .

So,

let

• length of the rectangular table = L = x/2 and
• width of rectangular = W = 3x

So, the area of the rectangular table A = LW

= x/2 × 3x

= 3x²/2

So, the simplified expression for the area of the rectangular table is Three-halves x squared, 3x²/2

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