Area of Right Triangle with Leg Ratio

Consider a right triangle where the lengths of the legs are in a ratio of 3:4. If the hypotenuse of this triangle is 25 units long, determine the lengths of the two legs and find the area of the triangle.

Let the lengths of the legs be represented as $3x$ and $4x$. According to the Pythagorean theorem:

$$ (3x)^2 + (4x)^2 = (25)^2 $$

Calculate the value of $x$ from this equation and subsequently find the area of the triangle using the formula:

$$ ext{Area} =\frac{1}{2} imes ext{base} imes ext{height} $$

Provide your answer in square units as a grid-in response.