A picture frame has a total perimeter of 2 meters. The height of the frame is .62 times its width. Find the dimensions of the frame.
h = 0.62*w
where h is height, w is width
P = 2*h + 2*w = 2 = 2*0.62*w + 2*w
solve for w, then use first equation to solve for h
Let's denote the width of the frame as "w" (in meters).
According to the given information, the height of the frame is 0.62 times its width, which means the height would be 0.62w.
The formula to calculate the perimeter of a rectangle is: Perimeter = 2(width + height)
Given that the total perimeter of the frame is 2 meters, we can set up the equation:
2 = 2(w + 0.62w)
Let's simplify the equation:
2 = 2(1.62w)
Now, solve for "w":
2 = 3.24w
Dividing both sides by 3.24:
w = 2/3.24
w ≈ 0.6173 meters
So, the width of the frame is approximately 0.6173 meters.
To find the height, we can substitute this value back into the equation height = 0.62w:
height ≈ 0.62(0.6173)
height ≈ 0.382 meters
Therefore, the dimensions of the frame are approximately 0.6173 meters for the width and 0.382 meters for the height.
To find the dimensions of the frame, we need to set up and solve a system of equations based on the given information.
Let's assume the width of the frame as 'w'. According to the problem, the height of the frame is 0.62 times its width, which means the height is 0.62w.
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this case, the total perimeter of the frame is given as 2 meters, so we can write the equation as:
2 = 2(w + 0.62w)
Simplifying this equation, we have:
2 = 2(1.62w)
Dividing both sides of the equation by 2 gives:
1 = 1.62w
Now, we can solve for w by dividing both sides of the equation by 1.62:
w = 1 / 1.62
Using a calculator, we find that w ≈ 0.617 meters.
Now we can find the height of the frame by multiplying the width by 0.62:
height = 0.62 * 0.617
Using a calculator, we find that the height ≈ 0.382 meters.
Therefore, the dimensions of the frame are approximately 0.617 meters in width and 0.382 meters in height.