For each of two rectangles, the length to width ratio is 3:2. The ratio of the length of the larger is 7:5. What is the ratio of the area of the two rectangles?
first:
length -- 3x
width --- 2x
area = 6x^2
2nd:
???
"The ratio of the length of the larger is 7:5"
don't know what that means
Ahaha ghee
To find the ratio of the area of the two rectangles, we need to know the individual lengths and widths of the rectangles. However, we can use the given information about the ratios to determine these values.
Let's assume that the length and width of the first rectangle are 3x and 2x, respectively. Since the length-to-width ratio is 3:2, we can set up the equation:
length of the first rectangle / width of the first rectangle = 3/2
(3x) / (2x) = 3/2
Simplifying the equation, we get:
3x / 2x = 3/2
3x × 2 = 2x × 3
6x = 6x
This equation confirms that the ratio of length to width in the first rectangle is 3:2.
Now let's move on to the second rectangle. We know that the ratio of the length of the larger rectangle to the first rectangle is 7:5. If the length of the first rectangle is 3x, using this ratio, we can set up the equation:
length of the second rectangle / length of the first rectangle = 7/5
length of the second rectangle / 3x = 7/5
Cross-multiplying, we get:
(3x) × (7/5) = (length of the second rectangle)
21x / 5 = (length of the second rectangle)
Therefore, the length of the second rectangle is (21x/5).
Now that we have the dimensions of both rectangles, let's calculate their areas:
Area of the first rectangle = length × width = (3x) × (2x) = 6x^2
Area of the second rectangle = length × width = (21x/5) × (2x) = (42x^2/5)
Finally, we can find the ratio of their areas:
Area of the first rectangle / Area of the second rectangle = (6x^2) / (42x^2/5)
Simplifying this expression, we divide the numerator and denominator by x^2:
Area of the first rectangle / Area of the second rectangle = (6/42) × (5/1)
Canceling out common factors, we get:
Area of the first rectangle / Area of the second rectangle = 1/7
Therefore, the ratio of the area of the two rectangles is 1:7.