The Correct Answer and Explanation is:
The correct answer is C. √200.
This problem involves a right-angled triangle where the two legs, the sides that form the right angle, are equal in length. Both legs are labeled with the variable ‘x’. The hypotenuse, which is the side opposite the right angle, has a length of 20. To find the value of ‘x’, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is a² + b² = c².
In this specific triangle, ‘a’ and ‘b’ are both ‘x’, and ‘c’ is 20. We can substitute these values into the theorem:
x² + x² = 20²
First, we combine the terms on the left side of the equation:
2x² = 20²
Next, we calculate the value of 20² (20 multiplied by 20), which is 400:
2x² = 400
To solve for x², we need to isolate it by dividing both sides of the equation by 2:
x² = 400 / 2
x² = 200
Finally, to find the value of ‘x’, we take the square root of both sides. Since length must be a positive value, we only consider the positive root:
x = √200
This result matches option C. For further simplification, √200 can be written as √(100 × 2), which equals 10√2. However, based on the choices provided, √200 is the expected answer.
