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? (1 point)
To find the area of the new triangle, we need to first find the dimensions of the new triangle.
Let's assume the dimensions of the original triangle are:
Base = b
Height = h
Since it is a right triangle, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
Given that the area of the original triangle is 13 m^2, we can write the equation as:
13 = (1/2) * b * h
To find the dimensions of the new triangle, we increase the original dimensions by a scale factor of 3:
New base = 3b
New height = 3h
To find the area of the new triangle, we use the same formula:
New area = (1/2) * new base * new height
Substituting the new dimensions into the formula:
New area = (1/2) * (3b) * (3h)
Simplifying:
New area = 9 * (1/2) * b * h
Since we know the original area is 13 m^2, we can substitute the original area into the equation:
New area = 9 * 13
Simplifying further:
New area = 117 m^2
Therefore, the area of the new triangle is 117 m^2.
To solve this problem, we need to understand how the area of a triangle changes when the dimensions are increased by a scale factor.
The area of a triangle is given by the formula: A = (1/2) * base * height.
Given that the original triangle has an area of 13 m2, let's denote the base of the original triangle as 'b' and the height as 'h'. So we have:
13 = (1/2) * b * h
Now, we are told that the dimensions of the triangle are increased by a scale factor of 3. This means that the new base and height will be three times the original dimensions. So we can say:
New base = 3b
New height = 3h
Now, let's calculate the area of the new triangle using the new dimensions:
New Area = (1/2) * (3b) * (3h)
= (1/2) * 3 * 3 * b * h
= 9 * (1/2) * b * h
= 9 * 13
= 117 m2
Therefore, the area of the new triangle is 117 m2.