The area A of a triangle is given by the formula A=1/2bh If the base of the triangle with height 12 inches is doubled, its area will be increased by 48 square inches. Find the base of the orignial triangle.
Doubling the base without changing the height would simply double the area.
So the increase is 48 square inches, which means the original triangle is 48 square inches.
48 = (1/2)base(12)
base = 8
To solve this problem, we will use the given information and the formula for the area of a triangle.
Let's start by writing down the information we have:
The formula for the area of a triangle is: A = (1/2)bh, where A is the area, b is the base, and h is the height.
We are given that the height is 12 inches and that if the base is doubled, the area is increased by 48 square inches.
Let's break down the problem step by step:
1. Let's start by finding the area of the triangle with the doubled base.
- Let the original base be represented by b.
- The doubled base will be 2b (since it is given that if the base is doubled).
- The height of the triangle is given as 12 inches.
- Using the formula for the area of a triangle, we can write the equation: A1 = (1/2)(2b)(12)
2. The problem states that if the base is doubled, the area is increased by 48 square inches.
- This means that the new area (A2) will be the original area (A1) plus 48: A2 = A1 + 48.
3. Now we can substitute the values into the equations we formed.
- For A1, we have A1 = (1/2)(2b)(12) = 12b.
- For A2, we have A2 = 12b + 48.
4. We know that A2 = A1 + 48, so we can equate the two expressions:
12b + 48 = 12b.
5. Now we can solve for the base (b):
48 = 0.
Since we obtained a contradiction (48 = 0), this means that our original assumption is incorrect. Therefore, there is no solution to the problem as it is given.