The image shows a table at a restaurant in the shape of a trapezoid. The restaurant owners want to determine if trapezoidal tables will fit comfortably into the rest of the dining room and a scale drawing of the table. If the greatest length of the table is represented in the scale drawing by 1.5 feet, what will the length of the other sides of the table be? Write your answer in decimal form.
Since the greatest length of the table is represented by 1.5 feet in the scale drawing, we can assume the length of the trapezoid is 1.5 feet.
Let's call the two other sides of the trapezoid x and y. Since we know that the longest side is 1.5 feet, the length of the other two sides will be less than 1.5 feet.
To find the relationship between the sides, we can use the formula for the perimeter of a trapezoid: P = x + 1.5 + y + 1.5.
Since the perimeter is the sum of all the sides, we have:
P = x + 1.5 + y + 1.5 = 1.5 + x + y
We can simplify this to:
P = 3 + x + y = 1.5 + x + y
Subtracting x and y from both sides, we get:
3 = 1.5
Therefore, x and y must be less than 1.5 feet. Since the perimeter of the table will be 1.5 feet, x and y must be less than 1.5 feet.
Therefore, the length of the other sides of the table will be less than 1.5 feet.