Answer :
Answer:
To find the value of the hypotenuse \( c \) in a right triangle where \( p = 5 \) (perpendicular) and \( b = 3 \) (base), you can use the Pythagorean theorem:
\[ c = \sqrt{p^2 + b^2} \]
Substitute the given values:
\[ c = \sqrt{5^2 + 3^2} \]
\[ c = \sqrt{25 + 9} \]
\[ c = \sqrt{34} \]
Therefore, the value of the hypotenuse \( c \) is \( \sqrt{34} \).
Step-by-step explanation:
We can find the hypotenuse using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides (base and height).
Let's denote the hypotenuse as h. We are given that p (base) = 5 and b (height) = 3.
So, according to the Pythagorean theorem:
h² = p² + b²
h² = 5² + 3²
h² = 25 + 9
h² = 34
Taking the square root of both sides to find h:
h = √34
Since the hypotenuse cannot have a negative length, h = √34. The answer is √34.