# A triangle has side lengths of 6, 8, and 10. Is it a right triangle? Explain.

###### Question:

## Answers

Your answer is 480 i think

[tex]\boxed{\textsf{ \textbf{ Yes} , the given triangle is a right angled triangle .}}[/tex]

Step-by-step explanation:

We are given three sides of the triangle and we need to say that whether the triangle is right Angled triangle or not . The given side lenghts are 6 cm , 8 cm and 10 cm . ( Units not given in Question ) .

[tex]\textsf{$\implies$ Sides = 6cm , 8cm and 10 cm .}[/tex]

So , a triangle with its given sides will be a right angled triangle if it has a right angle . And the sum of squares of two smallest sides must be equal to the square of the longest side . ( According to Pythagoras Theorem ) .

Here two smallest sides are 8cm and 6cm .

[tex]\implies\textsf{ $\sf Sides_{(smallest)}$= 8cm and 6 cm }[/tex]

And the largest side is 10 cm .

[tex]\sf\implies Side_{(largest)}= 10 cm[/tex]

And here the sum of squares of 8cm and 6cm should be equal to the square of 10cm in order to Prove it a right angled triangle .

[tex]\sf\implies (8cm)^2+(6cm)^2 = (10cm)^2 \\\\\sf\implies 64 cm^2+36cm^2 = 100 cm^2 \\\\\sf\implies \boxed{\pink{\frak{ 100 cm^2=100cm^2}}}[/tex]

Since LHS = RHS hence the triangle is a right angled triangle .

If a triangle is right angle triangle then,

it will satisfy the Pythagorean theorem.

i,e

[tex]\text{Longer side}^2 = \text{Sum of the square of two little side}[/tex]

As per he statement:

A triangle has side lengths of 6,8, and 10

Square of little sides are:

[tex]6^2 = 36[/tex]

[tex]8^2 = 64[/tex]

Sum of these square of little sides we have;

⇒[tex]36+64 =100[/tex]

Square of the longer side:

[tex]10^2 = 100[/tex]

⇒[tex]6^2+8^2 = 10^2[/tex]

so, it satisfy the given condition of right angled triangle

Therefore, a triangle with side length 6, 8 and 10 is a right angle triangle.

Step-by-step explanation:

Use the Pythagorean Theorem to test it.

6² + 8² ≟ 10²

36+64 ≟ 100

100 = 100

It is a right triangle.

This cant be determined

Step-by-step explanation:

There is no information about the angle of the line

Yes, because when the side lengths of a triangle are in the ratio 3: 4: 5, then it is a right triangle. These sides are 6: 8: 10, then the triangle is a right one.

Step-by-step explanation:

yes, it is a right triangle

step-by-step explanation:

remember: a triangle can only be a right triangle if it works with the pythagorean theoremtherefore, we can plug in the numbers we have in the formulaknow the formula: a^2 + b^2 = c^2now, plug ina^2 + b^2 = c^2

6^2 + 8^2 = 10^2

the largest side is always the hypotenusewe have to see if both sides equal to the same value6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

yes they are equal, therefore it is a right triangleYes,

Step-by-step explanation:

The Pythagorean theorem states that: In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

6² = 36

8² = 64

36 + 64 = 100

10² = 100

100 = 100 so it is a right triangle.

yes

Step-by-step explanation:

10x10=6x6 + 8x8

100= 36 + 64

Pythagoras theorem

D is the answer I’m pretty sure

you should at least use a calculater

step-by-step explanation:

[tex]Domain and range? does anyone know?[/tex]You have to give us options