A right-angle triangle is stretched so that the base of the triangle is twice as wide, but the height of the stretched triangle is half the height of the original. The area of the resulting triangle will be:

Question

larger than the original.

smaller than the original.

exactly double the original.

the same as the original.

Answer 1

The area of a triangle is given by the formula A = (1/2) * base * height.

Let's say the original base is b and the original height is h.

After stretching the triangle, the new base becomes 2b and the new height becomes (1/2)h.

Using the area formula for the stretched triangle, we have:

A(stretched) = (1/2) * (2b) * (1/2)h = (1/2)bh = (1/2) * A(original).

Therefore, the area of the resulting triangle is half of the original, so it is smaller than the original.

Therefore, the correct answer is: smaller than the original.