Comparing Areas of Triangle and Rectangle

Very Hard Quantitative Comparisons Geometry Comparisons

Consider a right triangle, Triangle XYZ, where the lengths of the legs are 9 units and 12 units. First, calculate the area of Triangle XYZ.

The area of a right triangle can be found using the formula:

$$ ext{Area} = rac{1}{2} imes ext{base} imes ext{height} $$

Next, compare the area of Triangle XYZ to the area of a rectangle that has a length of 10 units and a width of 8 units.

Calculate the area of the rectangle using the formula:

$$ ext{Area} = ext{length} imes ext{width} $$

Which of the following statements is true?

The area of Triangle XYZ is less than the area of the rectangle.

The area of Triangle XYZ is equal to the area of the rectangle.

The area of Triangle XYZ is greater than the area of the rectangle.

The area of Triangle XYZ is significantly smaller than the area of the rectangle.

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