A rectangle with an area of 32 inches squared has one side measuring 4 inches. A similar rectangle has an area of 288 inches squared. How long is the longer side in the larger rectangle?

To find the length of the longer side in the larger rectangle, we can set up a proportion using the given information:

First, let's find the length of the shorter side in the larger rectangle. We know that the area of the rectangle is 288 inches squared, and one side measures 4 inches. Therefore, the shorter side of the larger rectangle can be found by dividing the area by the length of the shorter side in the smaller rectangle:

Shorter side of the larger rectangle = Area of the larger rectangle / Length of the shorter side in the smaller rectangle
Shorter side of the larger rectangle = 288 inches squared / 4 inches
Shorter side of the larger rectangle = 72 inches

Now that we have the length of the shorter side in the larger rectangle, we can use this information to find the length of the longer side. Since the rectangles are similar, their corresponding sides are proportional. We can set up a proportion using the lengths of the corresponding sides in both rectangles:

Length of the longer side in the larger rectangle / Length of the shorter side in the larger rectangle = Length of the longer side in the smaller rectangle / Length of the shorter side in the smaller rectangle

Plugging in the values we have:

Length of the longer side in the larger rectangle / 72 inches = Length of the longer side in the smaller rectangle / 4 inches

Now, we can solve for the length of the longer side in the larger rectangle:

Length of the longer side in the larger rectangle = (Length of the longer side in the smaller rectangle / 4 inches) * 72 inches

To find the length of the longer side in the smaller rectangle, we can use the fact that the area of the smaller rectangle is 32 inches squared and the length of one side is 4 inches. Therefore, the length of the longer side in the smaller rectangle is:

Length of the longer side in the smaller rectangle = Area of the smaller rectangle / Length of the shorter side in the smaller rectangle
Length of the longer side in the smaller rectangle = 32 inches squared / 4 inches
Length of the longer side in the smaller rectangle = 8 inches

Plugging this value into the proportion:

Length of the longer side in the larger rectangle = (8 inches / 4 inches) * 72 inches
Length of the longer side in the larger rectangle = 2 * 72 inches
Length of the longer side in the larger rectangle = 144 inches

Therefore, the longer side in the larger rectangle is 144 inches.

Similar figures have corresponding sides, areas and perimeters in the same proportion.

32 : 288 = 4 : x
32/288 = 4/x
cross multiply
32x = 1152
x = ?