Final answer:
To solve for the dimensions of the rectangular room with a perimeter of 29 meters where the length is 1.4 times the width, two equations are set up. Solving these equations yields a width of 6.04 meters and a length of 8.46 meters.
Step-by-step explanation:
To find the dimensions of the rectangular room where the length is 1.4 times the width and its perimeter is 29 meters, we can set up the following equations using the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Step 1: Set up the equations
Let the width be x meters.
Then the length is 1.4x meters.
So the perimeter is 2(1.4x) + 2(x) = 29 meters.
Step 2: Solve for x (width)
2(1.4x) + 2x = 29
2.8x + 2x = 29
4.8x = 29
x = 29 / 4.8
x = 6.04 meters (rounded to two decimal places) - This is the width.
Step 3: Find the length
Length = 1.4(6.04)
Length = 8.456 meters (rounded to three decimal places)
Therefore, the dimensions of the room are a width of 6.04 meters and a length of 8.46 meters.