Question

What is the difference between the numerical values of the area of the triangle and the length of the hypotenuse of the triangle? A. 1 B. 5 C. 6 D. 7

Short answer

The difference between the numerical values of the area of the triangle and the length of the hypotenuse of the triangle is \(1\).

Step-by-step solution

Calculate the base and height from the given triangle

From the given triangle, we can see that the base and height have measures of 3 and 4, respectively. These will be used to calculate both the area and the hypotenuse length.

Calculate the area of the triangle

Using the area formula for a triangle: Area = (1/2) * base * height. Plugging in the base and height, we have: Area = (1/2) * 3 * 4 = (1/2) * 12 = 6

Calculate the hypotenuse length

Using the Pythagorean theorem: hypotenuse² = base² + height². Plugging in the base and height, we have: hypotenuse² = 3² + 4² = 9 + 16 = 25 Now, take the square root of both sides to find the length of the hypotenuse: hypotenuse = \(\sqrt{25}\) = 5

Calculate the difference between the area and the hypotenuse length

Now that we have the area of the triangle (6) and the length of the hypotenuse (5), we can find the difference: Difference = Area - Hypotenuse Length Difference = 6 - 5 = 1 The difference between the numerical values of the area of the triangle and the length of the hypotenuse of the triangle is 1. Therefore, the correct answer is: A. 1