The length of a rectangle is twice the width. The perimeter is 84 cm more than its width. Find the dimensions.
y = 2w
2w+2y = w+84
2w+4w = w + 84
5w = 84
w = 84/5
so, y=168/5
check:
2(w+y) = 2(252/5) = 504/5 = 84/5 + 84
Well, well, well! It seems we have a math problem on our hands. Let's put on our thinking cap and wrack our clown brains!
Let's suppose the width of the rectangle is "x" cm. According to the problem, the length of the rectangle is twice the width, so it would be 2x cm. Are you with me so far?
Now, let's calculate the perimeter of the rectangle. The formula for perimeter is P = 2(length + width). So, the perimeter would be 2(2x + x), which simplifies to 6x cm.
But wait, there's more! The problem also states that the perimeter is 84 cm more than its width, which means 6x = x + 84.
Now, we can solve this simple equation. Subtracting x from both sides, we get 5x = 84. Finally, dividing both sides by 5, we find that x = 16.8 cm.
So, the width of the rectangle is 16.8 cm, and the length (which is twice the width) would be 2 × 16.8 cm = 33.6 cm.
Voila! The dimensions of the rectangle are 16.8 cm by 33.6 cm.
Let's denote the width of the rectangle as "w".
To solve this problem, we can set up a system of equations based on the given information.
Let's start by assigning variables to the dimensions of the rectangle. Let's say the width of the rectangle is 'w' cm. Since the length is twice the width, we can express the length as '2w' cm.
We are also given that the perimeter is 84 cm more than the width. The perimeter of a rectangle can be calculated by adding the lengths of all four sides. In this case, it would be:
2w + 2(2w) = w + 84
Simplifying the equation, we have:
2w + 4w = w + 84
Combining like terms,
6w = w + 84
To isolate 'w' on one side of the equation, we subtract 'w' from both sides:
6w - w = 84
This simplifies to:
5w = 84
To find the value of 'w', we divide both sides by 5:
w = 84/5
w = 16.8
Now that we have the width, we can substitute this value back into one of our earlier equations to find the length:
Length = 2w = 2(16.8) = 33.6 cm
Therefore, the dimensions of the rectangle are width = 16.8 cm and length = 33.6 cm.