Question

Determine if the sides form a right triangle.

Answer 1

Answer:

Yes.

$\rule{70mm}{2pt}$

Step-by-step explanation:

To tackle such questions use the Pythagoras Theorem.

Provided a triangle whose sides are 3√2, 3√3 and 3√5 and are asked to check or determine if the sides form a right triangle or not.

We know that hypotenuse is the longest side. Let's call 3√5 = Hypotenuse side, 3√2 = Perpendicular and 3√3 = Base. So,

Using formula: (Hypotenuse)² = (Perpendicular)² + (Base)²

$\implies{\sf{(3\sqrt{5})^2 = (3\sqrt{2})^2 + (3\sqrt{3})^2}}$

$\implies{\sf{9(5) = 9(2) + 9(3)}}$

$\implies{\sf{45 = 18 + 27}}$

$\implies{\sf{45 = 45}}$

LHS = RHS

So, from above calculations we can say that the given sides form a right triangle.