5. The value of x is 10 cm.
6. The value of x is 12 in.
7. The value of x is 5 mi.
8. The value of x is 13 cm.
5. 6² + 8² = x²
This equation is based on the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides (legs).
Here, you are finding the hypotenuse (x) of a right triangle with legs of 6 and 8.
You correctly calculate:
6² = 36 (square 6)
8² = 64 (square 8)
36 + 64 = 100 (add the squares)
√100 = 10 (find the square root of the sum)
Therefore, the length of the hypotenuse (x) is 10.
6. 15² - 9² = x²
This equation is similar to the previous one, but instead of finding the hypotenuse, you are finding the length of a leg (x) of a right triangle with the hypotenuse of 15 and another leg of 9.
You correctly calculate:
15² = 225 (square 15)
9² = 81 (square 9)
225 - 81 = 144 (subtract the squares)
√144 = 12 (find the square root of the difference)
Therefore, the length of the leg (x) is 12.
7. 3² + 4² = x²
This equation again applies the Pythagorean theorem to find the hypotenuse (x) of a right triangle with legs of 3 and 4.
You correctly calculate:
3² = 9 (square 3)
4² = 16 (square 4)
9 + 16 = 25 (add the squares)
√25 = 5 (find the square root of the sum)
Therefore, the length of the hypotenuse (x) is 5.
8. 12² + 5² = x²
This follows the same pattern as the previous equations. You are finding the hypotenuse (x) of a right triangle with legs of 12 and 5.
You correctly calculate:
12² = 144 (square 12)
5² = 25 (square 5)
144 + 25 = 169 (add the squares)
√169 = 13 (find the square root of the sum)
Therefore, the length of the hypotenuse (x) is 13.