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

Answer:

$\sqrt{30}$

Step-by-step 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

${h}^{2} = {(3 \sqrt{2} )}^{2} + {(2 \sqrt{3} )}^{2}$

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

${h}^{2} = 9 \times 2 + 4 \times 3$

Multiply the numbers

${h}^{2} = 18 + 12$

Add the numbers

${h }^{2} = 30$

Take the square root of both sides of the equation

$h = \sqrt{30}$

Hope this helps...

Best regards!!

Answer 2

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

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