The lengths of the sides of a rectangle are in a ratio of 4:7. If the length is 31.5 in., find the width, perimeter and area of this rectangle.
4/7 - 31.5/W
4W = 220.5
W = 55.125
P = 2L + 2W
A = LW
4/7 = 31.5/W
4:7 as n:31.5
4/7=n/31.5
7n=126
n=18
P=2(18)+2(31.5)
A=18 x 31.5
To find the width of the rectangle, we need to use the ratio given. The ratio of the lengths of the sides is 4:7. We can set up a proportion to find the width:
Width / Length = 4 / 7
Since the length is given as 31.5 inches, we can substitute it into the proportion:
Width / 31.5 = 4 / 7
To solve for the width, we can cross-multiply and then divide:
Width = (31.5 * 4) / 7 = 18 inches
So, the width of the rectangle is 18 inches.
To find the perimeter of the rectangle, we need to add up the lengths of all the sides. Since opposite sides of a rectangle are equal, we can use the formula:
Perimeter = 2 * (Length + Width)
Plugging in the values, we get:
Perimeter = 2 * (31.5 + 18) = 99 inches
Therefore, the perimeter of the rectangle is 99 inches.
To find the area of the rectangle, we multiply the length by the width:
Area = Length * Width = 31.5 * 18 = 567 square inches
Therefore, the area of the rectangle is 567 square inches.