There is a rectangle, it's height is 3x and its width is 2x+xy. Find the area, but in the rectangle there are to empty boxes, there width and hight are x.

Question

What is the area, please let me know ASAP, can you show me what steps you need to take also when your solving the problem.

Answer 1

Hi Shivansh,

 

Step 1. If you draw a rectangle, you can label the height as 3x and the width as 2x+xy.  

 

Step 2. The area of the large rectangle is height multiplied by the width: 3x(2x + xy).  You can use the distributive property to simplify the terms: 3x(2x) + 3x(xy) = 6x² + 3x²y .

 

Step 3. To find the area of the two smaller boxes inside the rectangle, draw a line that separates the width into two parts, so that one part will have a width of 2x and the other part will have a width of xy.  The height, 3x, remains the same for both of the smaller boxes.

 

Therefore the area of the two boxes will be:

3x(2x) = 6x² and 3x(xy) = 3x²y, which are identical to the terms created when we distributed in step 2.

 

Hope that helps.