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Choose all situations that describe a right triangle.


A ladder 12 feet long leans against a wall. The top of the ladder is 8 feet above the ground. The bottom of the ladder is 6 feet from the wall.


A ladder 10 feet long leans against a wall. The top of the ladder is 6 feet above the ground. The bottom of the ladder is 8 feet from the wall.


A ladder 18 feet long leans against a wall. The top of the ladder is 9 feet above the ground. The bottom of the ladder is 12 feet from the wall.


A ladder 15 feet long leans against a wall. The top of the ladder is 12 feet above the ground. The bottom of the ladder is 9 feet from the wall.

Respuesta :

Answer:

We have a right triangle in cases 2 and 4

Step-by-step explanation:

In a right, we have to meet the condition of Pythagoras´ Theorem that is

L²  =  x²  +  y²        ( L is the hypotenuse and "x" and "y" the legs.

All the above descriptions have a right angle so we must check which of them meet Pythagoras´theorem requirement

1.-

(12)²  =  (8)² + (6)²     ⇒  144 > 64  + 36  so in this case we do not have a right triangle

2.-

(10)² = (6)² + (8)²    ⇒    100  = 36  + 64    We have here a description of a right triangle

3.-

(18)²  =  (9)²  + (12)²    ⇒  324  >  81 + 144    so in this case we do not have a right triangle

4.-

(15)²  =  (12)² + (9)²      ⇒ 225 = 144 + 81  We have here a description of a right triangle´

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