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In a 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg?

A. [tex]\( 2:1 \)[/tex]

B. [tex]\( \sqrt{2}:1 \)[/tex]

C. [tex]\( 1:1 \)[/tex]

D. [tex]\( 1:\sqrt{2} \)[/tex]

Sagot :

GinnyAnswer
Let's consider the properties of a 45-45-90 triangle.

In a 45-45-90 triangle, the two non-right angles are both 45 degrees. This specific triangle is a type of isosceles right triangle where the two legs are congruent, meaning they have the same length.

The hypotenuse of such a triangle is longer than the legs, specifically by a factor of [tex]\(\sqrt{2}\)[/tex]. However, when comparing the lengths of the legs to each other, since they are both congruent:

1. Let’s denote the length of each leg as [tex]\(a\)[/tex].
2. Since both legs have the same length, the ratio of the length of one leg to the length of the other leg is simply [tex]\(a : a\)[/tex].

By simplifying [tex]\(a : a\)[/tex], we get [tex]\(1 : 1\)[/tex].

Thus, the ratio of the length of one leg to the length of the other leg in a 45-45-90 right triangle is:
[tex]\[ \boxed{1:1} \][/tex]
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