Two triangles are similar. The ratio of their areas is 1:4. If the height of the smaller triangle is 3 cm, how long is the corresponding height of the larger triangle, in centimeters?
does this mean that i just multiply the numbers of the sides by four?
areas of similar figures area proportional to the square of their sides
area1/area2 = side1^2/side2^1
1/4 = side1^2/side2^2
4side1^2 = side2^2
take √ of both sides
2side1 = side2
so if one side is 3, the side of the larger square must be 6
check:
area of smaller is 3x3 = 9
area of larger is 6x6 = 36, which is in the ratio of 9/16 = 1:4
12
No, you cannot simply multiply the numbers of the sides by four to find the corresponding height of the larger triangle. In similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Therefore, in this case, if the ratio of the areas is 1:4, the ratio of the sides will be √(1:4), which simplifies to 1:2.
Since we know the height of the smaller triangle is 3 cm, the corresponding height of the larger triangle can be found by multiplying the height of the smaller triangle by the ratio of the sides.
So, the corresponding height of the larger triangle will be 3 cm × 2 = 6 cm.
No, multiplying the lengths of the sides by four would not give you the corresponding height of the larger triangle. To find the corresponding height, you need to understand that the ratio of areas between two similar figures is equal to the square of the ratio of their corresponding side lengths.
In this case, the ratio of the areas of the two triangles is given as 1:4. Since the area of a triangle is proportional to the product of its base and height, the ratio of the corresponding base lengths would also be 1:2.
Since you are given that the height of the smaller triangle is 3 cm, you can set up a proportion using the corresponding sides:
(height of larger triangle) / (height of smaller triangle) = (base length of larger triangle) / (base length of smaller triangle)
Let's denote the height of the larger triangle as 'h'.
So, h / 3 = (2nd triangle base length) / (1st triangle base length)
Since the ratio of base lengths is 1:2, the base length of the smaller triangle would be half of the base length of the larger triangle.
1st triangle base length = (2nd triangle base length) / 2
Now, substitute this relationship into the original equation:
h / 3 = [(2nd triangle base length) / 2] / (2nd triangle base length)
Simplifying, we get:
h / 3 = 1 / 2
Multiply both sides by 3:
h = 3 / 2 = 1.5 cm
Therefore, the corresponding height of the larger triangle is 1.5 centimeters.