William currently has a backyard square blue slate patio he is re-designing his patio and making it into a larger rectangle with a link that is 5 feet shorter than three times it’s width. Side X one of the original sides of look square is an integer. William decides that the perimeter should be no less than 80 feet.
a) Write an inequality to model the situation and solve it
b) what could be the smallest dimensions of the original square
c) using your answer to part B determine the least area and square feet of his new patio
the new rectangle has dimensions w by 3w-5
so, 2(w + 3w-5) ≥ 80
so, w ≥ 45/4
If he means to have the same area, then w(3w-5) ≥ (45/4)(3*45/4 - 5) ≈ 323.4
The smallest perfect square at least that big is 18^2 = 324