A rectangle has a length of 3.4 ft. and a width of 5.7 ft. A larger similar rectangle has a length of 17 ft. What is the width of the larger
rectangle?
To find the width of the larger rectangle, we can use the concept of similarity of shapes.
Two shapes are considered similar if their corresponding angles are equal and the ratios of their corresponding sides are equal.
In this case, we have two rectangles that are similar. We can set up a proportion to find the ratio between their lengths:
Length of larger rectangle / Length of smaller rectangle = 17 ft. / 3.4 ft.
Simplifying this proportion, we get:
Length of larger rectangle / 3.4 ft. = 17 ft. / 3.4 ft.
Now, we can solve for the length of the larger rectangle:
Length of larger rectangle = (17 ft. / 3.4 ft.) * 3.4 ft.
Length of larger rectangle = 17 ft.
Since the length of the larger rectangle is 17 ft., we can use the same ratio to find the width of the larger rectangle:
Width of larger rectangle / Width of smaller rectangle = Length of larger rectangle / Length of smaller rectangle
Width of larger rectangle / 5.7 ft. = 17 ft. / 3.4 ft.
Simplifying this proportion, we get:
Width of larger rectangle / 5.7 ft. = 5
Now, we can solve for the width of the larger rectangle:
Width of larger rectangle = 5 * 5.7 ft.
Width of larger rectangle = 28.5 ft.
Therefore, the width of the larger rectangle is 28.5 ft.