Answer & Step-by-step explanation:
To solve this problem, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In the triangle given, we can see that the lengths of the two shorter sides are 8 cm and 10 cm. We want to find the length of the hypotenuse.
Using the Pythagorean theorem, we can set up the equation:
a² + b² = c²
where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse.
Substituting in the values we know, we get:
8² + 10² = c²
Simplifying:
64 + 100 = c²
164 = c²
Taking the square root of both sides, we get:
c = sqrt(164)
c ≈ 12.8062
Therefore, the length of the hypotenuse is approximately 12.8062 cm.