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Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm? acute, because 62 + 102 < 122 acute, because 6 + 10 > 12 obtuse, because 62 + 102 < 122 obtuse, because 6 + 10 > 12

Respuesta :

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The Pythagoras theorem states that
the sum of squares of the shorter sides (legs) of a right triangle equals the square of the third side.

A corollary from the same theorem helps us solve this problem:
If the sum of the squares of the shorter sides of a triangle is greater than the square of the third side, the included angle is acute.  ..... (case 1)
Conversely, if the sum of the squares of the shorter sides of a triangle is less than the square of the third side, the triangle is obtuse.  .....(case 2)

Here we have
6^2+10^2 = 36+100=136 <12^2=144
Therefore case 2 applies, and the triangle is obtuse.

The given triangle whoe sides are 6cm, 10cm, and 12cm is an obtuse triangle and it can be determine by using pythagorian theorem.

Given :

The side lengths of a triangle are: 6cm, 10cm, and 12cm.

Pythagorian theorem can be used to find out that the triangles are acute or obtuse. According to pythagorian theorem, the sum of square of shorter side is equal to the square of the third side of the right angle triangle.

According to pythagorian theorem:[tex]\rm (Hypotenuse)^2 = (Perpendicular)^2+(Base)^2[/tex]. That is, [tex]\rm H^2 = P^2+B^2[/tex].

There are some rules to find the triangle is obtuse or acute:

  • If [tex]\rm P^2+B^2<H^2[/tex] than the triangle is obtuse.
  • If [tex]\rm P^2+B^2>H^2[/tex] than the triangle is acute.

Now, applying pythagorian theorem:

[tex]6^2+10^2=12^2[/tex]

[tex]36+100=144[/tex]

136 = 144

Here, it is clearly observe that 136 <  144 therefore, the triangle is obtuse.

For more information, refer the link given below:

https://brainly.com/question/24252852

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