Question

if a right triangle has one side measuring 3√2 and another side measuring 2√3, what is the length of the hypotenuse?

Answer 1

`\small\star\underline\bold\red{Given-}`

Sides of the right triangle

• 2√3 (p)
• 3√2 (b)

`\small\star\underline\bold\red{To\:Find-}`

• Third side (hypotenuse)

`\small\star\underline\bold\red{Solution-}`

By Pythagoras Theorum ,

`\small\fcolorbox{red}{white}{h² = b² + p² }`

`\implies` h² = (2√3)² + (3√2)²

`\implies` h² = 12 + 18

`\implies` h² = 30

`\implies` h = √30

Answer 2

`√(30)`

Explanation:

Given,

Perpendicular ( p ) = 3√2

Base ( b ) = 2√3

Hypotenuse ( h ) = ?

Now, let's find the length of the hypotenuse:

Using Pythagoras theorem:

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

plug the values

`{h}^(2) = {(3 √(2) )}^(2) + {(2 √(3) )}^(2)`

To raise a product to a power, raise each factor to that power

`{h}^(2) = 9 * 2 + 4 * 3`

Multiply the numbers

`{h}^(2) = 18 + 12`

Add the numbers

`{h }^(2) = 30`

Take the square root of both sides of the equation

`h = √(30)`

Hope this helps...

Best regards!!