The length of a rectangle is 4 times its width. If the perimeter of the rectangle is 70 ft., find the area.
70 = 2(4W) + 2W
70 = 10W
7 = W
A = 7 * 4 * 7
To find the area of a rectangle, we need to know its length and width. In this case, we are given that the length of the rectangle is 4 times its width.
Let's assume the width of the rectangle is "w". Therefore, the length of the rectangle is 4w.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 70 ft. Since the opposite sides of a rectangle are equal in length, we can set up an equation to find the dimensions of the rectangle.
Perimeter = 2(length + width)
Substituting the given values:
70 = 2(4w + w)
Simplifying the equation:
70 = 2(5w)
Dividing both sides of the equation by 2:
35 = 5w
Now, solving for w:
w = 35/5
w = 7 ft
Using the width, we can find the length:
Length = 4w = 4 * 7 = 28 ft
Now that we know the length and width of the rectangle, we can find the area.
Area of a rectangle = Length * Width
Area = 28 ft * 7 ft
Area = 196 square ft
Therefore, the area of the rectangle is 196 square feet.