Answer:
7 by 11
Explanation:
Let's assume that the length of the rectangular patio is "l" meters and the width is "w" meters.
According to the problem statement, the perimeter of the patio is 36 meters, so we can set up the equation:
2l + 2w = 36
Simplifying this equation by dividing both sides by 2, we get:
l + w = 18
We also know that the area of the patio is 77 square meters, so we can set up another equation:
lw = 77
We now have two equations in two variables, and we can use them to solve for l and w.
From the first equation, we can solve for one variable in terms of the other:
w = 18 - l
Substituting this expression for w into the second equation, we get:
l(18 - l) = 77
Expanding the left-hand side, we get a quadratic equation:
18l - l^2 = 77
Rearranging and simplifying, we get:
l^2 - 18l + 77 = 0
This quadratic equation can be factored as:
(l - 7)(l - 11) = 0
Therefore, the solutions are l = 7 or l = 11.
If l = 7, then w = 18 - l = 11, and the dimensions of the patio are 7 meters by 11 meters.
If l = 11, then w = 18 - l = 7, and the dimensions of the patio are 11 meters by 7 meters.
Therefore, the dimensions of the patio are either 7 meters by 11 meters or 11 meters by 7 meters.