△ABC is an isosceles right triangle with legs measuring 1 inch each. How long is the hypotenuse?

Question

Geometry Question

Answer 1

Hi Julia, an isosceles right triangle with legs measuring 1 inch each has a hypotenuse of √2.

 

Reason:

 

The isosceles right triangle has two equal angles. The total number of degrees in any triangle is 180 degrees. The right triangle is 90 degrees.

 

Subtract 90 from 180 gives 90 degrees. Divide 90 by 2 gives 45 degrees.

 

For any isosceles right triangle, the relationship of the legs to the hypotenuse, is 1, 1, and the √2. 

 

Example: if the legs are 3 inches, then the hypotenuse would be 3√2.

 

Or use the Pythagorean Theorem: 

 

a² + b² = c²

 

Substituting for a and b:

 

1 + 1 = c²

 

c² = 2

 

c = ±√2

 

However, the legs of a triangle cannot be negative, so discard the negative solution.

 

Answer: √2

 

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