A right-angle triangle is stretched so that the base of the triangle is half as wide, but the hypotenuse is twice the length of the original. The area of the resulting triangle will be:
A the same size as the original.
B larger than the original.
C exactly half the original.
D smaller than the original.
To solve this problem, we first need to determine the relationship between the sides of the original triangle and the sides of the resulting triangle after they have been stretched.
Let's denote the original base as "b" and the original hypotenuse as "h". According to the problem, after stretching, the new base is half as wide, so it becomes (1/2)b. The hypotenuse, on the other hand, becomes twice the length of the original, so it becomes 2h.
Now, let's calculate the areas of the original triangle and the resulting triangle.
The area of the original triangle is given by (1/2)bh, where b is the base and h is the height. Since the original triangle is a right-angle triangle, the height is equal to the length of the other leg.
The area of the original triangle = (1/2)bh
The area of the resulting triangle is given by (1/2)(1/2)b(2h), where (1/2)b is the new base and 2h is the new height.
The area of the resulting triangle = (1/2)(1/2)b(2h) = (1/4)(2bh) = (1/2)bh
Therefore, the area of the resulting triangle is equal to the area of the original triangle.
So, the correct answer is: A) the same size as the original.