A right triangle has an area of 24 ft^2 the demesions of the triangle are increased by a scale factor of 6 what is the area of the new triangle
the new dimensions are
6w and 6h, so the area is 24 * 6^2
not a choice
To find the area of the new triangle, we first need to determine the dimensions of the new triangle after being scaled up by a factor of 6.
Given that the original triangle has an area of 24 ft², we can use the formula for the area of a right triangle:
Area = (base * height) / 2
Let's assume the original base and height of the right triangle are b and h respectively.
So, our equation becomes:
24 = (b * h) / 2
Simplifying the equation, we get:
48 = b * h
Now, since the dimensions of the triangle are increased by a scale factor of 6, we can express the new base and height as 6b and 6h, respectively.
Applying the same formula to the new triangle, we have:
New Area = (6b * 6h) / 2
Simplifying further, we get:
New Area = (36b * 6h) / 2
New Area = 18b * 6h
New Area = 108bh
So, the area of the new triangle is 108 times the area of the original triangle.
Now, substituting the value of b * h from our earlier equation, we get:
New Area = 108 * 48
New Area = 5184 ft²
Therefore, the area of the new triangle is 5184 ft².