A right triangle has an area of 13 m^2. The dimensions of the triangle are increased by a scale factor of 3. What is the area of the new triangle?
A) 39 m^2
B) 169 m^2
C) 117 m^2
D) 142 m^2
I think it is B
You do not square the area. You square the scale factor.
area scales by the square of the linear scale factor, since
a = 1/2 bh
if everything is scaled by 3, that gives you
1/2 (3b)(3h) = 1/2 * 9bh = 9(1/2 bh) = 9a = 9*13 = 117 m^2
To find the area of the new triangle, we need to calculate the area of the original triangle and then apply the scale factor of 3 to get the new area.
Let's assume the dimensions of the original triangle are base (b) and height (h). The area of a right triangle is given by the formula: A = (1/2) * b * h.
Given that the area of the original triangle is 13 m^2, we have:
13 = (1/2) * b * h
Now, we are given that the dimensions of the triangle are increased by a scale factor of 3. This means the new dimensions are 3b and 3h. Now, let's find the new area by using these new dimensions.
New area = (1/2) * (3b) * (3h) = 9 * (1/2) * b * h = 9 * original area
Therefore, the area of the new triangle is 9 times the area of the original triangle.
To find the area of the new triangle, multiply the original area by 9:
New area = 13 * 9 = 117 m^2
So, the correct answer is C) 117 m^2.
To solve this problem, we need to understand how the area of a right triangle is related to its dimensions. The formula to calculate the area of a right triangle is:
Area = (base * height) / 2
Let's assume the original dimensions of the right triangle are b and h. Therefore, the original area can be expressed as:
13 = (b * h) / 2
Next, we are told that the dimensions of the triangle are increased by a scale factor of 3. This means the new dimensions are 3b and 3h.
To find the area of the new triangle, we can substitute the new dimensions into the area formula:
New Area = (3b * 3h) / 2 = (9bh) / 2
Since we don't have the exact values for b and h, we cannot calculate the exact area. However, we can compare the relative change in area between the two triangles.
The ratio of the new area to the original area is:
(9bh / 2) / (bh / 2) = (9bh * 2) / (bh * 2) = 9
Therefore, the area of the new triangle is 9 times the area of the original triangle.
Since the original triangle has an area of 13 m^2, the new triangle will have an area of 13 * 9 = 117 m^2.
So, the correct answer is C) 117 m^2.