Marissa is designing a rectangular poster whose width is 2/3 of its height. Its perimeter will be 100 inches. what are the dimensions of the poster?
h + w = 50
w = (2/3) h
(5/3) h = 50
h = 30
w = 20
To find the dimensions of the rectangular poster, we can set up an equation based on the given information.
Let's say the height of the poster is represented by "h" inches.
According to the problem, the width is 2/3 of the height, which means the width is (2/3) * h inches.
The perimeter of a rectangle is given by the formula: P = 2 * (length + width)
In this case, the perimeter is given as 100 inches, so we can write the equation as:
100 = 2 * (h + (2/3) * h)
Now, let's simplify and solve for "h":
100 = 2 * (3h/3 + 2h/3)
100 = 2 * (5h/3)
100 = 10h/3
To isolate "h", we can multiply both sides of the equation by 3/10:
(3/10) * 100 = (3/10) * (10h/3)
30 = h
Therefore, the height of the poster is 30 inches.
Now, we can substitute the value of "h" back into the equation for the width:
Width = (2/3) * h
Width = (2/3) * 30
Width = 20 inches
Therefore, the dimensions of the poster are 30 inches (height) and 20 inches (width).