A rectangle has a width of 4 inches and a length of 6 inches. A similar rectangle has a width of 12 inches. What is the length of the similar rectangle?
the width is 3 times as big, so the length is also.
To find the length of the similar rectangle, we can use the concept of similarity between two shapes. Similar shapes have proportional side lengths.
In this case, we can set up a proportion using the width and length of the two rectangles:
Width of Rectangle 1 / Length of Rectangle 1 = Width of Rectangle 2 / Length of Rectangle 2
Plugging in the values we know:
4 inches / 6 inches = 12 inches / Length of Rectangle 2
To isolate the length of the similar rectangle, we can use cross-multiplication:
(4 inches)(Length of Rectangle 2) = (6 inches)(12 inches)
Now, we can solve for the length of the similar rectangle:
(4 inches)(Length of Rectangle 2) = (6 inches)(12 inches)
4(Length of Rectangle 2) = 72 inches
To solve for Length of Rectangle 2, we divide both sides of the equation by 4:
Length of Rectangle 2 = 72 inches / 4
Length of Rectangle 2 = 18 inches
Therefore, the length of the similar rectangle is 18 inches.