SOLUTION: A larger rectangle has another, smaller rectangle inscribed within it. The larger rectangle has sides given by the equation 3x2 + 7x + 6 and 5x + 4. The inner rectangle has side

Algebra ->  Triangles -> SOLUTION: A larger rectangle has another, smaller rectangle inscribed within it. The larger rectangle has sides given by the equation 3x2 + 7x + 6 and 5x + 4. The inner rectangle has side      Log On


   

Question 630360: A larger rectangle has another, smaller rectangle inscribed within it. The larger rectangle has sides given by the equation 3x2 + 7x + 6 and 5x + 4. The inner rectangle has sides given by 2x2 + 4x + 3 and 2x + 1.

Calculate the area between the two rectangles.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A larger rectangle has another, smaller rectangle inscribed within it.
The larger rectangle has sides given by the equation 3x2 + 7x + 6 and 5x + 4.
The inner rectangle has sides given by 2x2 + 4x + 3 and 2x + 1.
Calculate the area between the two rectangles.
:
Find the areas
d = %28%283x%5E2%2B7x%2B6%29%2A%285x%2B4%29%29 - %28%282x%5E2%2B4x%2B3%29%2A%282x%2B1%29%29
dif in area = large rect area - small rec area
d = %2815x%5E3%2B47x%5E2%2B58x%2B24%29 - %284x%5E3%2B10x%5E2%2B10x%2B3%29
remove brackets
d = 15x%5E3%2B47x%5E2%2B58x%2B24+-+4x%5E3-10x%5E2-10x-3
combine like terms
d = 15x%5E3-4x%5E3%2B47x%5E2-10x%5E2%2B58x-10x%2B24-3
d = 11x%5E3%2B37x%5E2%2B48x%2B21 sq/units