posted by Jane on .
A rectanglar blacktop with a length of 5x and a width of 3x has been erected inside a rectangular field that has a length of 12x and a width of 7x.
What is the area of the part of the field that is not blacktop? (I believe the answer is 69x^2)
There is a circular fountain in the rectangular field that has a radius of 3x. What is the area of the part of the field that does not include the blacktop of the fountain? Factor your answer. (Please show me how to set up and solve) Thanks
5x3 = 15
12x7 = 84
84-15 is 69, so you are corect
area of circle is pi(3x)^2 = 9pi x^2
so, subtract: 84x^2 - 9pi x^2 = (84-9pi)x^2
the factor of part b. would end up being 3x^2(23-3pi). because you would have to bring down the area of part a. which would be 69x^2 with the 9pix^2 not 84, therefore, giving the factored solution of 3x^2(23-3pi). 3 is the gcf because 69 cannot and 9 cannot be multiplyed to obtain each with the same nuber other than 3.