A ratio is a comparison of two quantities. If we consider two quantities a and b, the ratio a:b indicates that there are a units of the first quantity for every b units of the second quantity.
B
How is the first quantity compared with the second quantity?
We want to find the ratio of the length of the blue rectangle to the length of the green rectangle. Recall that a ratio is a comparison of two quantities. If we consider two quantities a and b, the ratio a: b indicates that there are a units of the first quantity for every b units of the second quantity.
a/b or a: b
Since we want to compare the lengths of both rectangles, we can substitute a= 3 and b= 6 into the expression to obtain the length ratio.
3/6 or 3: 6Now, we will the same for the width. In this case, a= 2 and b= 4.
The next step is calculate the ratio of the perimeters. To do so, recall that the perimeter of a rectangle is the sum of the side lengths of the rectangle.
P= l + w + l +w → P=2l + 2w
Let's substitute the given values into the formula to find the perimeter of each rectangle, starting with the blue rectangle.
Now that we have the value of perimeters, we can write the ratio between them.
10:20
Next, we want to find the ratio of the areas. To do so, let's use the formula for the area of a rectangle.
A=l * w
For the blue rectangle we have l= 3 and w= 2.
Length&: 2:4
Width&: 3:6
Perimeter&: 10:20
Area&: 6:24
Notice that in the ratios for length, width, and perimeter, the second quantity is twice the fist quantity.
rclc
Length:& 2:4 & ⇒ & 2:(2)2
Width:& 3:6 & ⇒ & 3:(2)3
Perimeter:& 10:20 & ⇒ & 10:(2)10
This is because all these quantities are linear. The ratio of the area is different because the area is a quadratic quantity.
