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Which of the following shows the length of the third side, in inches, of the triangle below?

A right triangle is shown. One side of the triangle is labeled as 74 inches. The height of the triangle is labeled as 24 inches.

Square root of 6052 inches
50 inches
70 inches
Square root of 98 inches

Respuesta :

MsRay

Answer:

Without an actual drawing to show which side is 74 inches, then the answer could either be the square root of 6052 inches OR 70 inches.  

Step-by-step explanation:

All right triangles follow the rule of the pythagorean theorem, which states that a^2 + b^2 = c^2, where 'a' and 'b' represent the legs of a triangle and 'c' represents the hypotenuse.  The legs of a right triangle are the two sides that come together to form the 90 degree angle and the hypotenuse is the angled line across from the 90 degree angle.  In this case, the height would have to represent one of the legs, while the other 'side' would need to represent either a leg or the hypotenuse (depending on the actual diagram presented which is not shown in the problem posted).  So, if you substitute the values given into our legs, or 'a' and 'b', you would end up with the value of 'c' as the square root of 6052.  However, if the given side is actually the hypotenuse, you would solve by subtracting the c^2 from a^2 to get 'b'=70 inches.  

The height of the right angle triangle is 70 inches

Using Pythagoras's theorem for right angle triangle

c²  = a² + b²

where

c = hypotenuse

a and b are the other 2 legs.

Therefore,

c = 74 inches

a = 24 inches

74² = 24² + b²

5476  = 576 + b²

5476 - 576 = b²

b² = 4900

square root both sides

b = √4900

b = 70 inches

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