Q66. - Algebra 2

Question

BASKETBALL

Use the diagram of an NCAA basketball court below.

66. Illustrate the Distributive Property by writing two expressions for the area of the basketball court.

Step-by-Step Solution

Answer

Two expressions to represent the area are

$\left(47\times 50\right)+\left(47\times 50\right)$ and $\left(47+47\right)\times 50$

Step 1 - Observations from image

Breadth of the basketball court is 50 ft

Length of the half side of basketball court is 47 ft each.

Step 2 - Write first expression

Since, Area (A) of a court with given length (l) and breadth (b) is 

$A=l\times b$

So area of given court is sum of area of two half sides

$A=\left(47\times 50\right)+\left(47\times 50\right)$

Step 3 - Write second expression

For any real numbers a, b, and c distributive property is 

$a\left(b+c\right)=ab+ac\text{ and }\left(b+c\right)a=ba+ca$

For second expression, use distributive property in first expression

$A=\left(47+47\right)\times 50$