the lengths of corresponding sides of similar rectangles have a ratio of 7:4 the perimeter of the smaller rectangle is 80 ft. what is the peremiter of the larger rectangle?
(7/4)(80) = 140
To find the perimeter of the larger rectangle, we need to determine the ratio between their perimeters.
Since the lengths of the corresponding sides have a ratio of 7:4, we can assume that the ratio applies to all sides of the rectangles, including the widths. Let's assign variables to the lengths and widths of the rectangles.
Let's call the length of the smaller rectangle x, and its width y. Therefore, the ratio of the length to the width is 7:4.
According to the given information, the perimeter of the smaller rectangle is 80 ft.
Recall that the perimeter of a rectangle is the sum of all its sides: P = 2(length + width).
In this case, the perimeter of the smaller rectangle is 80 ft, so we can set up the equation:
80 = 2(x + y)
Now, we need to find the relationship between the lengths and widths of the larger rectangle using the given ratio.
Since the ratio of the lengths of the corresponding sides is 7:4, we can express the length of the larger rectangle as 7x and its width as 4y.
To find the perimeter of the larger rectangle, we can use the same formula:
P = 2(length + width)
P = 2(7x + 4y)
Now, let's substitute the values of x and y that we found earlier:
P = 2(7 * (x) + 4 * (y))
P = 2(7 * (80 - y) + 4 * (y)) (substituting the value of x from the equation 80 = 2(x + y))
P = 2(560 - 7y + 4y)
P = 2(560 - 3y)
P = 1120 - 6y
Therefore, the perimeter of the larger rectangle is 1120 - 6y.