Question

find the value of x.

x =

tell whether the side lengths form a pythagorean triple.
yes
no

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 27\), \(b = 36\), and \(c=x\) (hypotenuse).

$$x^{2}=27^{2}+36^{2}$$

Step2: Calculate the squares

$$27^{2}=729$$

,

$$36^{2}=1296$$

So, \(x^{2}=729 + 1296\)

Step3: Sum the values

\(x^{2}=2025\)

Step4: Take the square root

\(x=\sqrt{2025}=45\)

Step5: Check if it is a Pythagorean triple

A Pythagorean triple consists of three positive integers \(a,b,c\) such that \(a^{2}+b^{2}=c^{2}\). Here, \(27,36,45\) are positive integers and \(27^{2}+36^{2}=45^{2}\) (since \(729+1296 = 2025\) and \(45^{2}=2025\))

Answer:

\(x = 45\), yes