The Mystery of the Right Triangle Area

What is the area of a right triangle with legs labeled as eight times x and seven times x if x = 4 cm?

A. 16 cm^2

B. 240 cm^2

C. 448 cm^2

D. 896 cm^2

Answer:

The correct area of the right triangle is 448 cm^2.

Right triangles are fascinating geometric figures that have specific properties when it comes to calculating their area. In this case, we are presented with a right triangle whose legs are labeled as eight times x and seven times x. Given that x is equal to 4 cm, we can easily determine the dimensions of the triangle.

First, we substitute the value of x into the expressions for the legs of the triangle. The base of the triangle, labeled as eight times x, becomes 8 * 4 cm = 32 cm. Meanwhile, the height of the triangle, labeled as seven times x, becomes 7 * 4 cm = 28 cm.

Next, we utilize the formula for calculating the area of a right triangle, which is 1/2 * base * height. By plugging in the values we found for the base and height, we get: Area = 1/2 * 32 cm * 28 cm = 448 cm^2.

Therefore, the area of the right triangle with legs labeled as eight times x and seven times x, when x is equal to 4 cm, is 448 cm^2. This calculation showcases the importance of understanding geometric formulas and how to apply them effectively.