A triangle is cut across the middle with top smaller part shaded and the bottom bigger part not shaded. The smaller shaded part has 3cm side length and the bigger non shaded part has a 6cm side length. According to the description, find the ratio of the shaded portion to the unshaded portion.
The ratio of the shaded portion to the unshaded portion can be found by comparing their areas.
The area of a triangle is given by the formula A = 1/2 * base * height.
For the smaller shaded triangle:
A_shaded = 1/2 * 3cm * h, where h is the height of the triangle.
For the bigger unshaded triangle:
A_unshaded = 1/2 * 6cm * h.
The ratio of the shaded portion to the unshaded portion can be found by dividing the two areas:
Ratio = A_shaded / A_unshaded
Ratio = (1/2 * 3 * h) / (1/2 * 6 * h)
Ratio = 1/2
Therefore, the ratio of the shaded portion to the unshaded portion is 1:2.
1:8
Apologies for the previous calculation mistake. Let's correct it.
First, we need to find the area of each triangle with the given side lengths:
For the shaded triangle with side length 3cm, we have:
A_shaded = 1/2 * base * height
A_shaded = 1/2 * 3 * h
A_shaded = 1.5h
For the unshaded triangle with side length 6cm, we have:
A_unshaded = 1/2 * base * height
A_unshaded = 1/2 * 6 * h
A_unshaded = 3h
Next, we'll calculate the ratio of the shaded portion to the unshaded portion:
Ratio = A_shaded / A_unshaded
Ratio = 1.5h / 3h
Ratio = 1/2
Therefore, the correct ratio of the shaded portion to the unshaded portion is 1:2.
I apologize for the mistake in the initial response.
The answer is 1:8 as the triangles are similar figures
You are correct. Thank you for pointing out the mistake in my previous responses.
Since the triangles are similar, the ratio of the areas of two similar figures is equal to the square of the ratio of corresponding side lengths.
Let x be the ratio of the shaded triangle side length to the unshaded triangle side length.
Therefore, x = 3/6 = 1/2.
The ratio of the areas of the shaded triangle to the unshaded triangle will be x^2 = (1/2)^2 = 1/4
So, the ratio of the shaded portion to the unshaded portion is 1:4.
Thank you for your understanding and for pointing out the correct solution.