Answer:
Explanation:
To find the length of the longer leg of a right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).
In this case, the shorter leg is given as 5 cm, and the hypotenuse is given as 8 cm.
Let's denote the length of the longer leg as x.
According to the Pythagorean theorem, we have the equation:
5^2 + x^2 = 8^2
Simplifying the equation, we get:
25 + x^2 = 64
Subtracting 25 from both sides of the equation, we have:
x^2 = 64 - 25
x^2 = 39
To find the value of x, we take the square root of both sides of the equation:
x = √39
Therefore, the length of the longer leg of the right triangle is approximately √39 cm.
Looking at the answer choices, we can see that option B, √39 cm, matches our calculated value.
So, the correct answer is:
B. √39 cm