Question

Find the third side in simplest radical form:
25

Answer 1

`\boxed{ \bold{24}}`

Explanation:

`\mathsf{given}`

`\mathsf{hypotenuse(h) = 25}`

`\sf{perpendicular (p) = 7}`

`\sf{base(b) = }`?

Now, Using Pythagoras theorem

`\sf{{h}^(2) = {p}^(2) + {b}^(2) }`

plug the values

⇒
`\sf{ {25}^(2) = {7}^(2) + {b}^(2) }`

Evaluate the power

⇒
`\sf{625 = 49 + {b}^(2) }`

Swap the sides of the equation

⇒
`\sf{49 + {b}^(2) = 625}`

Move constant to right hand side and change it's sign

⇒
`\sf{ {b}^(2) = 625 - 49}`

Calculate the difference

⇒
`\sf{ {b}^(2) = 576}`

Squaring on both sides

⇒
`\sf{b = 24}`

Hope I helped!

Best regards!