Final answer:
To find the area of the rectangle, use the Pythagorean theorem to find the width of the rectangle and then multiply the length and width together. In this case, the area of the rectangle is 432cm^2.
Step-by-step explanation:
To find the area of the rectangle, we need to multiply its length by its width. In this case, the length is given as 24cm and the diagonal is given as 30cm. We can use the Pythagorean theorem to find the width of the rectangle.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides. In this case, the diagonal acts as the hypotenuse and the length and width of the rectangle act as the other two sides.
Using the Pythagorean theorem, we can solve for the width of the rectangle: width^2 + length^2 = diagonal^2. Plugging in the values, we get width^2 + 24^2 = 30^2. Simplifying the equation, we get width^2 + 576 = 900. Subtracting 576 from both sides, we get width^2 = 324. Taking the square root of both sides, we get width = 18cm.
Now that we know the length and width of the rectangle, we can find its area by multiplying them together: Area = length * width = 24cm * 18cm = 432cm^2.