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Which equation can be used to find [tex]\( x \)[/tex], the length of the hypotenuse of the right triangle?

A. [tex]\( 18 + 24 = x \)[/tex]
B. [tex]\( 18^2 + 24 = x \)[/tex]
C. [tex]\( (18 + 24)^2 = x^2 \)[/tex]
D. [tex]\( 18^2 + 24^2 = x^2 \)[/tex]

Sagot :

GinnyAnswer
To find the length of the hypotenuse, [tex]\( x \)[/tex], of a right triangle with legs of length 18 and 24, we use the Pythagorean theorem. The Pythagorean theorem states:

[tex]\[ a^2 + b^2 = c^2 \][/tex]

where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the lengths of the legs of the triangle, and [tex]\( c \)[/tex] is the length of the hypotenuse.

In this problem, given:
- [tex]\( a = 18 \)[/tex]
- [tex]\( b = 24 \)[/tex]

We substitute these values into the Pythagorean theorem to find [tex]\( x \)[/tex]:

[tex]\[ 18^2 + 24^2 = x^2 \][/tex]

The correct equation is:

[tex]\[ 18^2 + 24^2 = x^2 \][/tex]

Therefore, the correct answer is:

[tex]\[ 18^2 + 24^2 = x^2 \][/tex]
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