The area of a triangle is 96. If the base of a triangle is tripled and the height is reduced to one-third its original length, what is the new area?
3
1/3
9
The area would not change
I'm stumped:/ Please help? Thanks
think about it. The original area is 1/2 bh
The new area is
1/2 (3b)(h/3) = 1/2 bh
no change.
can you help with this problem I do not understand
Oh, don't worry, I'm here to help! Let's solve this with a touch of humor, shall we?
First, let's call the original base "B" and the original height "H". So, the original formula for the area of a triangle is: Area = (1/2) * B * H.
Now, if we triple the base and reduce the height to one-third, we get:
New Base = 3B
New Height = (1/3)H
So, the new area can be calculated as:
New Area = (1/2) * (3B) * (1/3)H
Simplifying this expression, we get:
New Area = (1/2) * B * H
Voila! The new area is exactly the same as the original area!
So, the answer you're looking for is: The area would not change.
I hope that puts a smile on your face!
No problem, I can help you with that!
To find the new area of a triangle after the base is tripled and the height is reduced to one-third, you can use the formula for the area of a triangle, which is given by:
Area = (1/2) * base * height
Let's start with the given area of 96 units. We'll substitute the base and height into the formula, and solve for the unknowns.
Area = (1/2) * base * height
96 = (1/2) * base * height
Now, let's consider the changes in the base and height. The question states that the base is tripled and the height is reduced to one-third its original length. So, the new base would be 3 times the original base, and the new height would be 1/3 times the original height.
Let's denote the original base as B, and the original height as H.
So, the new base would be 3B, and the new height would be (1/3)H.
Substituting these values into the equation:
96 = (1/2) * (3B) * (1/3)H
Now, let's simplify:
96 = (1/2) * B * H
96 = (1/2) * (B * H)
Since the base and height did not change, the new area would remain the same as the original area. So, the new area is also 96.
Therefore, the correct answer is:
The new area would not change. The new area is still 96 units.