Question

The side lengths of a triangle are 9, 12, and 15. Is this a right triangle?

Answer 1

Answer:

$\boxed{Yes.}$

Step-by-step explanation:

To solve this equation, we can use the Pythagorean Theorem: $a^2 + b^2 = c^2$, where $a$ and $b$ are regular side lengths and $c$ is the hypotenuse.

• The hypotenuse is the longest side of a triangle and is assigned to the $c$-variable.
• The other two side lengths can be assigned to either $a$ or $b$ because of the commutative property: $a + b = b + a$.

Now, just substitute the side lengths into the formula and solve!

$9^2 + 12^2 = 15^2$    Simplify the equation by taking each value to its power.

$81 + 144 = 225$    Simplify by adding like terms.

$225 = 255$

Therefore, this is indeed a right triangle.

Answer 2

Answer:

Yes, this is a right triangle.

Step-by-step explanation:

Hypotenuse always have the highest number than base and perpendicular.

Hypotenuse ( h ) = 15

Base ( b ) = 9

Perpendicular ( p ) = 12

Let's see whether the given triangle is a right triangle or not

Using Pythagoras theorem:

${h}^{2} = {p}^{2} + {b}^{2}$

Plugging the values,

${15}^{2} = {12}^{2} + {9}^{2}$

Evaluate the power

$225 = 144 + 81$

Calculate the sum

$225 = 225$

Hypotenuse is equal to the sum of perpendicular and base.

So , we can say that the given lengths of the triangle makes a right triangle.

Hope this helps..

Best regards!!