Comparison of Areas in Right Triangles

Medium Quantitative Comparisons Geometry Comparisons

In a right triangle, the lengths of the legs are given as $a$ and $b$. Another triangle is formed by connecting the midpoints of the legs of the original triangle. If the lengths of the legs of the original triangle are 6 units and 8 units, compare the area of the original triangle with the area of the triangle formed by the midpoints of the legs.

The area of a triangle can be calculated using the formula: $$ ext{Area} = rac{1}{2} imes ext{base} imes ext{height}$$. Here, the base is one leg of the triangle and the height is the other leg.

Please select the correct comparison:

The area of the original triangle is greater than the area of the triangle formed by the midpoints.

The area of the original triangle is equal to the area of the triangle formed by the midpoints.

The area of the original triangle is less than the area of the triangle formed by the midpoints.

The area of the triangle formed by the midpoints cannot be determined.

Hint

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