for what values of x is the area of the rectangle greater than the area of the triangle?

Question

Rectangle length = 12, width = x+2

Triangle base = x+16, height = 10

Answer 1

Area of Rectangle = length*width

Rectangle area = 12(x+2) = 12x + 24

 

Area of triangle = (1/2)base*height

Triangle area = (1/2)10(x+16) = 5(x+16) = 5x + 80

 

You want to know for what values of x make

the area of the rectangle greater than that of the triangle:

 

12x+24>5x+80    subtract 5x from both sides

7x + 24 > 80       subtract 24 from both sides

7x > 56               divide both sides by 7

x > 8

 

All values larger than 8