Comparing Areas: Triangle ABC and Rectangle

Very Hard Quantitative Comparisons Geometry Comparisons

Consider a right triangle ABC where angle C is the right angle. The lengths of sides AC and BC are 7 units and 24 units, respectively.

Calculate the length of side AB using the Pythagorean theorem, which states:

$$c^2 = a^2 + b^2$$

where $c$ is the length of the hypotenuse, and $a$ and $b$ are the lengths of the other two sides.

Next, compare the area of triangle ABC to the area of a rectangle that has a length equal to side AC and a width equal to side BC.

What can you conclude about the areas of triangle ABC and the rectangle?

The area of the triangle ABC is greater than the area of the rectangle.

The area of the triangle ABC is equal to the area of the rectangle.

The area of the triangle ABC is less than the area of the rectangle.

The areas of the triangle ABC and the rectangle cannot be determined.

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