Final answer:
To find the dimensions of the rectangular dining room, we can use the given information about the area and perimeter. Using the equations for area and perimeter, we can solve a system of equations to find the values of length and width. The dimensions of the dining room are 4 meters by 5 meters.
Step-by-step explanation:
To find the dimensions of the rectangular dining room, we need to use the given information.
Let's assume the length of the dining room is x meters and the width is y meters.
According to the given information, the area is 20 square meters, so we have the equation:
x * y = 20
Since the perimeter is 18 meters, we have another equation:
2x + 2y = 18
Now, we can solve the system of equations to find the values of x and y:
2x + 40/x = 18.
2x^2 + 40 = 18x. Rearrange to form a quadratic equation:
2x^2 - 18x + 40 = 0.
Factor the quadratic equation or use the quadratic formula to find the solutions for x:
x = 4 or x = 5.
Now, substitute these values of x back into the equation y = 20/x to find the corresponding values for y:
When x = 4, y = 20/4 = 5.
When x = 5, y = 20/5 = 4.
Therefore, the dimensions of the dining room are 4 meters by 5 meters.