Two rectangles are similar. The first is 4in. wide and 15in. long. The second is 9in. wide. Find the length of the second rectangle.
Similar polygons have corresponding sides in the same ratio, so
4/15 = 9/x
4x=135
x = 135/4 or 33.75
the 2nd side is 135/4
check:
9 : (135/4)
=36:135
= 4 : 15
= 20:27
To find the length of the second rectangle, we can set up a proportion using the sides of the two rectangles.
In a pair of similar rectangles, the corresponding sides are proportional. This means that the ratio of the length of the first rectangle to the length of the second rectangle is equal to the ratio of the width of the first rectangle to the width of the second rectangle.
Let's set up the proportion using the given information:
Length of first rectangle / Length of second rectangle = Width of first rectangle / Width of second rectangle
Substituting the given values:
15in / Length of second rectangle = 4in / 9in
Now, we can solve for the length of the second rectangle by cross-multiplying and then dividing:
15in * 9in = 4in * Length of second rectangle
135in^2 = 4in * Length of second rectangle
To isolate the Length of the second rectangle, we need to divide both sides of the equation by 4in:
Length of second rectangle = 135in^2 / 4in
Simplifying the expression:
Length of second rectangle = 33.75in
Therefore, the length of the second rectangle is 33.75 inches.