Question - Calculating the Missing Side of a Right Triangle
Solution:
The triangle shown in the image appears to be a right triangle, with one side labeled 9, the other side labeled 18, and the hypotenuse labeled x. To find the missing side x, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. The Pythagorean theorem can be written as:c² = a² + b²where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. Plugging in the given values:x² = 9² + 18²x² = 81 + 324x² = 405Now, take the square root of both sides to solve for x:x = √405To simplify the square root of 405, you would look for perfect square factors of 405. The number 405 can be factored into 81 * 5, and since 81 is a perfect square (9 * 9), you can rewrite √405 as:x = √(81 * 5)x = √81 * √5x = 9 * √5Therefore, the missing side x is 9√5 units long.
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