I am doing corrections and I have no idea how to do this problem.
A right triangle has an area of 13 m2. The dimensions of the triangle are increased by a scale factor of 3. What is the area of the new triangle?
the area increases by a factor of 3^2
consider that the area is 1/2 bh
If b and h both grow by a factor of three, the new area is
1/2 (3b)(3h) = 1/2 bh * 3^2
So, the new area is 9*13 m^2
Thank you @Steve!!
To solve this problem, you need to understand the relationship between the areas of similar figures and the scale factor.
1. Start by calculating the area of the original triangle.
Since the area of the right triangle is given as 13 m², this is equal to 1/2 times the base times the height. So, we have:
13 m² = 1/2 * base * height
2. Now, let's consider the scale factor of 3. When you increase the dimensions of a figure by a scale factor of 3, all its linear dimensions (length, width, height) are multiplied by 3.
3. Apply the scale factor to the original triangle to determine the dimensions of the new triangle.
If the original triangle has base = b and height = h, then the new triangle will have base = 3b and height = 3h.
4. Calculate the new area of the triangle.
The area of the new triangle can be found in the same way as in Step 1, using the dimensions of the new triangle:
New Area = 1/2 * (3b) * (3h)
= 4.5 * b * h
= 4.5 * original area
= 4.5 * 13 m²
Therefore, the area of the new triangle is 4.5 * 13 m² = 58.5 m².