For each of two rectangles, the length to width ratio is 3:2. The ratio of the length of the larger rectangle to the length of the smaller rectangle is 7:5. What is the ratio of the area of the two rectangles?
ahh, I see you corrected it
1st:
length -- 3x
width ---2x
area = 6x^2
2nd :
lenth : width = 3y : 2y
area = 6y^2
but length of larger : length of smaller = 7:5
3y : 3x = 7 : 5
y/x = 7/5
y = 7x/5
so area of 2nd = 6(7x/5) = 294x^2/25
larger area / smaller area
= (294x^2/25) / 6x^2
= 49/25 or 49:25
or
simply realize that the area of similar figures is proportional to the square of their sides, which would be
7^2/5^2
= 49/25
The ratio of the length of a rectangle to the weight of the rectangle is 5:2 if the link is 45 centimeters what is the width of the rectangle in centimeters
Let's assume the length of the smaller rectangle is 3x and the width is 2x.
Therefore, the length of the larger rectangle is 7y and the width is 5y, where y is a common factor.
The area of the smaller rectangle is (3x)(2x) = 6x^2.
The area of the larger rectangle is (7y)(5y) = 35y^2.
To find the ratio of the area of the two rectangles, we divide the area of the larger rectangle by the area of the smaller rectangle.
So, the ratio of the area of the larger rectangle to the smaller rectangle is (35y^2)/(6x^2).
Please note that since no specific values are given for x and y, we cannot simplify the ratio further. Thus, the ratio is (35y^2)/(6x^2).
To find the ratio of the areas of the two rectangles, we first need to calculate the lengths and widths of the rectangles.
Let's assume the length of the smaller rectangle is 3x, and its width is 2x. Since the length to width ratio is 3:2, we can express the length and width of the smaller rectangle as 3x and 2x, respectively.
Now, we know that the larger rectangle has a length ratio of 7 to 5 compared to the smaller rectangle. Therefore, the length of the larger rectangle would be (7/5) multiplied by the length of the smaller rectangle, which is (7/5) * 3x = 21x/5.
Since the length to width ratio of the larger rectangle is also 3:2, we can calculate the width of the larger rectangle by multiplying the width of the smaller rectangle by (3/2). Therefore, the width of the larger rectangle is (3/2) * 2x = 3x.
Now that we have the lengths and widths of both rectangles, we can calculate their areas.
The area of the smaller rectangle is length multiplied by width, which is 3x * 2x = 6x^2.
The area of the larger rectangle is length multiplied by width, which is (21x/5) * 3x = (63/5)x^2.
To find the ratio of the areas, we divide the area of the larger rectangle by the area of the smaller rectangle:
((63/5)x^2) / (6x^2) = (63/5)/(6) = 63/30 = 21/10.
Therefore, the ratio of the areas of the two rectangles is 21:10.