square and rectangle have same area. rectangle length is 5 inch more than 2c the length of the same side. the width is 6 inch less than side. what is the length

Question

It is an algebra 2 quadratic applications review question

Answer 1

The area of a rectangle is length times width.  The area of a square is the square of its side length.  A square has sides of equal length.

 

For square:

 

width = x

length = x

 

 

For rectangle:

 

width = x - 6

length = 2x + 5

 

 

Now we set up the equation for area.

 

x² = (x - 6)(2x + 5)

 

Solve for x.

 

x² = 2x² - 7x - 30

 

 

Subtract x² on both sides of the equation.

 

0 = x² - 7x - 30

 

 

Factor the equation using FOIL, if possible.

 

0 = (x - 10)(x + 3)

 

 

   x = 10        and         x = -3

 

 

Since we cannot have a negative value for dimensions, we accept the positive value of x:

 

x = 10

 

Finally, you just plug in this value of x to find the length of the rectangle.