Question

real - world word problem write and solve three challenging area word problems requiring how to find the area of a rectangle. one example must include the distributive property.

Explanation:

Step1: First problem

A rectangular garden has a length of 12 meters and a width of 8 meters. What is its area?
The formula for the area of a rectangle is $A = l\times w$.
So, $A=12\times8 = 96$ square - meters.

Step2: Second problem

A rectangular room has a length that is 3 more than twice its width. If the width is 5 feet, what is the area of the room?
Let the width $w = 5$ feet. The length $l=2w + 3$. Substitute $w = 5$ into the length formula: $l=2\times5+3=10 + 3=13$ feet.
Using the area formula $A=l\times w$, we have $A = 13\times5=65$ square - feet.

Step3: Third problem (using distributive property)

A rectangle has a length of $(x + 4)$ units and a width of 6 units. Find its area.
Using the area formula $A=l\times w$, we get $A=(x + 4)\times6$.
By the distributive property $a(b + c)=ab+ac$, here $a = 6$, $b=x$, $c = 4$.
So $A=6\times x+6\times4=6x + 24$ square - units.

Answer:

Problem 1: Area is 96 square - meters.
Problem 2: Area is 65 square - feet.
Problem 3: Area is $6x + 24$ square - units.