math
posted by mark on .
The old lion cage at the zoo was a square, with sides x meters long. For the part of the zoo's 50 birthday celecration, the zoo expanded the length and width. The expression for the total area of the new cage is (x^2+18x+81) square meters.
Part 1:Robert thinks that the cage's length had increased by 6 meters, and its width increased by 8 meters. Is Robert right?
Part 2:How much did the zoo expand the length and width?
Part 3:If the area of the old lion cage was 25 square meters, what is the area of the new cage?
I'm not sure what are the answers are. For part 1, I think Robert is wrong, because i used factoring and 6+8=14 and 6 x 8=48.
For part 2, I think the length and width are 9.
Part 3, i don't have an answer for that.

Since x^2 + 18 x + 81 = (x+9)^2, the cage must still be square and increased in length of each side by 9 meters. That answers (1) and (2).
(3) If the old area was 25 m^2, the old side length a was sqrt 25 = 5 m.
Now it is 5 + 9 = 14 m