The area of the smllaer of two similar triangles is 1/9 the area of the larger triangle.
Suppose one side of the triangle is 3.6m. What is the length of the corresponding side of the larger triangle? Suppose one side of the larger triangle is 36m. What is the length of the corresponding side of the smaller triangle?
If the areas are in a 1:9 ratio, the corresponding side lengths are in a 1:3 ratio.
If a side length os the smaller triangle is 3.6 m, the larger triangle must have a corresponding side length of 10.8 m.. and so forth.
To find the length of the corresponding side of the larger triangle, we can use the concept of similarity. Similar triangles have proportional side lengths.
Let's denote the length of the corresponding side of the smaller triangle as x.
According to the given information, the ratio of the area of the smaller triangle to the larger triangle is 1/9. Since the area of a triangle is proportional to the square of its side lengths, we can say:
(area of smaller triangle) / (area of larger triangle) = (side length of smaller triangle)^2 / (side length of larger triangle)^2
1/9 = (x^2) / (36^2)
To find the length of the corresponding side of the larger triangle, we need to solve for x.
Cross-multiplying this equation, we get:
9 * (x^2) = 1 * (36^2)
9x^2 = 1296
Dividing both sides by 9, we have:
x^2 = 144
Taking the square root of both sides, we find:
x = 12
Therefore, the length of the corresponding side of the larger triangle is 12 meters.
Now, let's find the length of the corresponding side of the smaller triangle when one side of the larger triangle is 36 meters.
Using the same concept of similarity, we can set up the proportion:
(side length of smaller triangle) / (side length of larger triangle) = (area of smaller triangle) / (area of larger triangle)
Let's denote the length of the corresponding side of the smaller triangle as y.
Using the given information, the ratio of the area of the smaller triangle to the larger triangle is 1/9:
y / 36 = 1/9
Cross-multiplying, we get:
9y = 36 * 1
9y = 36
Dividing both sides by 9, we find:
y = 4
Therefore, the length of the corresponding side of the smaller triangle is 4 meters.