in a rectangle the measures of the base and the altitude are in a ratio of 1:4. I f the rectangle is equal in area to a square with a perimeter of 60 feet, find the dimensions of the rectangle
HELP PLEASE TYSM!!
square: 4s=60
s=15
area=15^2=225
rectangle
area= s * 4s=4s^2=225
s=1/2 55=55/2
4s=110
To find the dimensions of the rectangle, we can follow these steps:
Step 1: Calculate the side length of the square
Given that the square's perimeter is 60 feet, we can divide it by 4 to find the length of each side. So, 60/4 = 15 feet.
Step 2: Calculate the area of the square
The area of a square is given by the formula side length squared. Thus, the area of the square is 15^2 = 225 square feet.
Step 3: Set up the ratio between the base and altitude of the rectangle
The ratio between the base and altitude of the rectangle is given as 1:4. Let's assume the base is x, which means the altitude will be 4x.
Step 4: Calculate the area of the rectangle
The area of a rectangle is given by the formula length multiplied by width. In this case, since the rectangle is equal in area to the square, the area would be 225 square feet.
So, we have:
x * 4x = 225
Step 5: Simplify and solve the equation for x
4x^2 = 225
Divide both sides of the equation by 4:
x^2 = 56.25
Take the square root of both sides:
x = √56.25
x ≈ 7.5 feet
The base of the rectangle is approximately 7.5 feet, and the altitude will be 4 times that, so the altitude would be approximately 30 feet.
Therefore, the dimensions of the rectangle are approximately 7.5 feet by 30 feet.