The length of a rectangle is 8.75 cm more than 3 times the width. If the perimeter of the rectangle is 89.5 cm, what are its dimensions
Let's assume that the width of the rectangle is "x" cm.
Thus, the length of the rectangle is 3x + 8.75 cm.
The perimeter of a rectangle is found by adding the lengths of all four sides.
In this case, the length is added twice and the width is added twice: P = 2(length) + 2(width).
So,
89.5 = 2(3x + 8.75) + 2x.
Using the distributive property and combining like terms:
89.5 = 6x + 17.5 + 2x.
Continuing to simplify:
89.5 = 8x + 17.5.
Subtracting 17.5 from both sides:
89.5 - 17.5 = 8x.
72.0 = 8x.
Dividing both sides by 8:
9.0 = x.
Therefore, the width of the rectangle is x = 9.0 cm and the length is 3x + 8.75 = 3(9.0) + 8.75 = 27.0 + 8.75 = 35.75 cm.
Let's assume the width of the rectangle is "w" cm.
According to the problem, the length of the rectangle is 8.75 cm more than 3 times the width, which can be written as:
Length = 3w + 8.75 cm
To find the perimeter of the rectangle, we sum up all four sides:
Perimeter = 2(Length + Width)
Substituting the values, we have:
89.5 cm = 2((3w + 8.75 cm) + w)
Now, let's solve the equation step-by-step to find the value of "w":
1. Simplify the equation:
89.5 cm = 2(4w + 8.75 cm)
2. Distribute the 2 on the right side:
89.5 cm = 8w + 17.5 cm
3. Subtract 17.5 cm from both sides:
89.5 cm - 17.5 cm = 8w
4. Simplify the left side:
72 cm = 8w
5. Divide both sides by 8:
9 cm = w
Now that we have the width, let's calculate the length:
Length = 3w + 8.75 cm
Length = 3(9 cm) + 8.75 cm
Length = 27 cm + 8.75 cm
Length = 35.75 cm
Therefore, the width of the rectangle is 9 cm, and the length is 35.75 cm.
To find the dimensions of the rectangle, we'll set up equations based on the given information. Let's denote the width of the rectangle as "w" and the length as "l".
We're told that the length of the rectangle is 8.75 cm more than 3 times the width:
l = 3w + 8.75
We also know that the perimeter of a rectangle is the sum of all its sides. In this case, the perimeter is given as 89.5 cm:
2(l + w) = 89.5
Now we can solve these two equations simultaneously to find the width and length of the rectangle.
Substituting the first equation into the second equation:
2((3w + 8.75) + w) = 89.5
Simplifying:
2(3w + 8.75 + w) = 89.5
2(4w + 8.75) = 89.5
8w + 17.5 = 89.5
8w = 89.5 - 17.5
8w = 72
w = 72 / 8
w = 9
Substituting the value of w back into the first equation:
l = 3(9) + 8.75
l = 27 + 8.75
l = 35.75
So, the width of the rectangle is 9 cm and the length is 35.75 cm.