the ratio of area of two rectangles field is 25/9
(a)find the ratio of their length
(b)the small field is 20m long find the corresponding length of the larger cone
the lengths are in the ratio
√(25/9) = 5/3
1.. 25:9
2.. 5:216
1... 25:9
2... 5:216
To find the ratio of the lengths of two rectangles when the ratio of their areas is given, we can use the square root of the ratio of their areas.
(a) Ratio of Lengths:
Let's assume the length of the smaller rectangle is L1 and the length of the larger rectangle is L2.
The area ratio is given as 25/9, which means:
(L2^2) / (L1^2) = 25/9
Taking the square root of both sides of the equation to find the ratio of lengths:
L2 / L1 = √(25/9) = 5/3
So, the ratio of their lengths is 5/3.
(b) Corresponding Length:
We are given that the length of the smaller field is 20m. Let's assume the length of the larger field is L2.
Since we already found the ratio of lengths in part (a), we can set up a proportion to find the corresponding length:
L2 / 20 = 5/3
To solve for L2, we cross multiply and solve for L2:
3L2 = 20 * 5
3L2 = 100
L2 = 100 / 3
Therefore, the corresponding length of the larger field is approximately 33.33 meters.