A rectangular picture frame has a perimeter of 3f.The width of the frame is 0.62 times its height.Find the height of the frame.
Perimeter p = 2w + 2L
L = length (you called height)
0.62L = width
p = 3'
p = 2w + 2L
3 = 2L + 2(0.62L)
3 = 2L + 1.24L
Solve for L (height)
Let's assume the width of the frame is represented by "w", and the height is represented by "h".
Given that the perimeter of the frame is 3f, we can write this as an equation:
2w + 2h = 3f
Since the width of the frame is 0.62 times its height, we can write this as another equation:
w = 0.62h
Now we can substitute the value of w in the first equation:
2(0.62h) + 2h = 3f
Simplifying this equation gives us:
1.24h + 2h = 3f
3.24h = 3f
Now, to find the height of the frame, we can divide both sides of the equation by 3.24:
h = 3f / 3.24
Therefore, the height of the frame is equal to 3f divided by 3.24.
To find the height of the frame, we can set up a system of equations based on the given information.
Let's denote the width of the frame as W and the height as H.
We are given that the perimeter of the rectangular frame is 3f. The formula for the perimeter of a rectangle is P = 2W + 2H, where P is the perimeter, W is the width, and H is the height.
So, we can write the equation as:
2W + 2H = 3f (Equation 1)
We are also given that the width of the frame is 0.62 times its height, which can be expressed as:
W = 0.62H (Equation 2)
Now, we can substitute Equation 2 into Equation 1 to solve for the height.
2(0.62H) + 2H = 3f
1.24H + 2H = 3f
3.24H = 3f
H = 3f / 3.24
H = f / 1.08
Therefore, the height of the frame is f / 1.08.