Rectangle ABCD is 12 inches long and has a perimeter of 54 inches. Rectangle LMNO is similar to rectangle ABCD and is 2.4 feet long. What is the width of the rectangle LMNO?
Perimeter ABCD = 54
L = 12 in
Perimeter LMNO = x
L = 2.4 ft = 28.8 in
P = 2w + 2L
Use Ratio to find x (perimeter LMNO)
12/28.8 = 54/x
Cross multiply
12x = 1555.2
x = 129.6
LMNO P = 129.6
L = 28.8
P = 2w + 2L
129.6 = 2w + 2(28.8)
Solve for w, width of LMNO
To find the width of rectangle LMNO, we need to know the ratio of the lengths of rectangle ABCD and rectangle LMNO. Since both rectangles are similar, their corresponding sides are in proportion.
First, let's convert the length of rectangle LMNO from feet to inches. We know that 1 foot is equal to 12 inches, so 2.4 feet is equal to 2.4 x 12 = 28.8 inches.
Next, we need to find the ratio of the lengths of the two rectangles. The length of rectangle ABCD is given as 12 inches, and the length of rectangle LMNO is 28.8 inches. Therefore, the ratio of the lengths is 12/28.8.
Now, since the ratio of the lengths is the same as the ratio of the widths, we can use this ratio to find the width of LMNO. We know that the perimeter of rectangle ABCD is 54 inches, and the perimeter of a rectangle is given by the formula: perimeter = 2(length + width).
For rectangle ABCD, we have: 54 = 2(12 + width).
We can solve this equation to find the width of rectangle ABCD.
54 = 2(12 + width)
54 = 24 + 2width
2width = 54 - 24
2width = 30
width = 30/2
width = 15 inches.
So, the width of rectangle ABCD is 15 inches.
Finally, we can find the width of rectangle LMNO by applying the ratio of the lengths. Since the ratio of the lengths of ABCD and LMNO is 12/28.8, the ratio of the widths will also be 12/28.8.
Now we can solve for the width of LMNO:
width of LMNO = (width of ABCD)/(ratio of lengths)
= 15 / (12/28.8)
= 15 x 28.8 / 12
= 36 inches.
Therefore, the width of rectangle LMNO is 36 inches.