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.
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The height of a triangle with base b and area A is given by the formula h = 2a/b.
What is the height of a triangle with area 26 cm2 and base 8 cm?
To solve this problem, we can use the formula for the area of a triangle, which states that the area (A) is equal to half the product of the base (b) and the height (h): A = 1/2 * b * h.
Let's start by identifying the known information:
- Given: The height (h) is 12 inches.
- Given: If the base (b) is doubled, the area (A) increases by 48 square inches.
Using the formula for the area of a triangle, we can write the equation:
A = 1/2 * b * h
Now, we can plug in the given values:
A + 48 = 1/2 * (2b) * 12
Simplifying the equation, we have:
A + 48 = b * 12
Next, we need to isolate the base (b) on one side of the equation. To do this, we'll move the constant term (48) to the other side:
A = b * 12 - 48
Now, we can substitute the formula for A in terms of b and solve for b:
1/2 * b * h = b * 12 - 48
Multiplying both sides of the equation by 2 to eliminate the fraction:
b * h = 2 * (b * 12 - 48)
Simplifying further:
b * h = 2b * 12 - 96
Distributing the 2:
b * h = 24b - 96
Next, we can substitute the given height (h = 12) into the equation:
b * 12 = 24b - 96
Expanding the equation:
12b = 24b - 96
To get all the b terms on one side, we subtract 24b from both sides:
12b - 24b = -96
Simplifying:
-12b = -96
Now, let's isolate b by dividing both sides of the equation by -12:
b = (-96) / (-12)
Dividing -96 by -12:
b = 8
Therefore, the base of the original triangle is 8 inches.