the length of a rectangle is equal to triple the width. which system of equations can be used to find the dimensions of the rectangle if the perimeter is 85 centimeters?
To find the dimensions of the rectangle, we can set up a system of equations based on the given information.
Let's assume that the width of the rectangle is denoted by "w" centimeters. According to the problem, the length of the rectangle is equal to triple the width, so the length can be denoted as "3w" centimeters.
The formula for the perimeter of a rectangle is:
Perimeter = 2*(Length + Width)
From the given information, we know that the perimeter is 85 centimeters. Substituting the values, we can write the equation as:
85 = 2*(3w + w)
Now, we can simplify and solve this equation to find the value of "w" (the width) and then substitute it back to find the length. Let's solve the equation step-by-step:
85 = 2*(3w + w)
85 = 2*(4w) (combine like terms inside parentheses)
85 = 8w (multiply 2 and 4w)
8w = 85 (divide both sides by 8)
w = 10.625
Now that we know the value of "w" which is 10.625 cm, we can substitute it into the equation for the length:
Length = 3w = 3 * 10.625 = 31.875 cm
Therefore, the dimensions of the rectangle are approximately 10.625 cm (width) and 31.875 cm (length).
y=3x
2(x+y)=85