A rectangular piece of art is 4 meters wide and 6 meters long. It is surrounded by a uniform sidewalk. If the area of the uniform sidewalk is 39 square
(4+2w)(6+2w) - 4*6 = 39
Wow, that's a lot of sidewalk! Sounds like you're paving the way to greatness! But let's take a closer look at the area to make sure we don't clown around.
The rectangular piece of art is 4 meters wide and 6 meters long. If we add the same width of sidewalk around all sides, the dimensions of the larger rectangle would be (4 + 2x) meters wide and (6 + 2x) meters long. Here, x represents the width of the sidewalk.
Now, we know that the area of the uniform sidewalk is 39 square meters. So, we can set up an equation to solve for x:
(4 + 2x) * (6 + 2x) = 39
But hey, let's not get too carried away with math! Why did the artist bring a pencil to the art gallery? Because they wanted to draw some attention, of course!
Okay, okay, back to business. Solving the equation, we find that x is equal to 2. Therefore, the width of the uniform sidewalk is 2 meters.
Now that we have the width of the sidewalk, we can find the area of the whole set-up:
(4 + 2(2)) * (6 + 2(2)) = 8 * 10 = 80 square meters.
So, the total area of the rectangular piece of art and the sidewalk is 80 square meters. Talk about having a wide canvas to work with!
To find the width of the uniform sidewalk, we need to first find the total area of the rectangular piece of art and the sidewalk combined.
1. Calculate the area of the rectangular piece of art:
Area = Length × Width
Area = 6 meters × 4 meters
Area = 24 square meters
2. Calculate the total area of the rectangular piece of art and the sidewalk:
Total Area = Area of rectangular piece of art + Area of sidewalk
Total Area = 24 square meters + 39 square meters
Total Area = 63 square meters
3. Since the sidewalk is uniform, the width of the sidewalk on each side would be the same. Let's assume the width of the sidewalk on each side is represented by "x" meters.
4. To find the width of the sidewalk, we can subtract the width of the rectangular piece of art from the total width.
Total Width = Width of rectangular piece of art + 2 × Width of sidewalk
Total Width = 4 meters + 2x
Setting up an equation using the total area:
(4 meters + 2x) × 6 meters = 63 square meters
5. Solve for x:
24 meters + 12x = 63 square meters
Subtract 24 from both sides:
12x = 63 - 24
12x = 39
Divide both sides by 12:
x = 39 / 12
x ≈ 3.25
Therefore, the width of the uniform sidewalk is approximately 3.25 meters.
To solve this problem, we need to find the width of the sidewalk around the rectangular piece of art.
Let's represent the width of the sidewalk as 'x'.
The width of the art piece including the sidewalk would be equal to the sum of the art piece's width and twice the width of the sidewalk. Therefore, the total width would be '4 + 2x'.
Similarly, the length of the art piece including the sidewalk would be equal to the sum of the art piece's length and twice the width of the sidewalk. Therefore, the total length would be '6 + 2x'.
Now, we can determine the area of the entire rectangular piece of art including the sidewalk. It is calculated by multiplying the new width (4 + 2x) by the new length (6 + 2x). The area is given as 39 square meters.
So, (4 + 2x) × (6 + 2x) = 39.
Expanding this equation, we get 24 + 8x + 12x + 4x^2 = 39.
Combining like terms, we have 4x^2 + 20x + 24 = 39.
Rearranging the equation, we get 4x^2 + 20x - 15 = 0.
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula.
After solving for x, we can substitute the value obtained back into the equation 4 + 2x to find the width of the sidewalk.