Question

This is confusion please help

Answer 1

c = 5√5

Explanation:

When we have a right triangle, there is a property about its measurements that is always true, and its called the "Pythagorean Theorem"

First, let's understand the basic terms we use to describe the sides of a triangle:

we can call one leg "a", the other leg "b" and the slanted side "c"

("c" is also called the hypotenuse--and it's always opposite the 90-degree angle)

the pythagorean theorem:

a² + b² = c²

here, our "a" is 5, our "b" is 10 {and we don't know what c is}

let's try plugging these values into our formula:

a² + b² = c²

5² + 10² = c²

25 + 100 = c²

125 = c²

now, we know what c² is--but we want to know c,

so we must take the square root of both sides

√125 = √c²

√125 = c

now, while √125 is our answer, we can simplify further!

this is because 125 can be made up of 5 · 25

so,
`√(125) = √(5*25)`

and

`√(5*25)=√(5)*√(25)`

we can take out the square root of 25 (5):

`=√(5)*5`

we write this as such:
`5√(5)`

so, in simplest radical form, c = 5√5

(√125)

hope this helps!! have a lovely day :)