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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 :

GinnyAnsweridn
To determine the length of the hypotenuse [tex]\( x \)[/tex] of a right triangle, we use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse [tex]\( x \)[/tex] is equal to the sum of the squares of the lengths of the other two sides.

Given:
- One leg of the triangle is 18 units.
- The other leg of the triangle is 24 units.

According to the Pythagorean theorem, [tex]\( a^2 + b^2 = c^2 \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the lengths of the legs, and [tex]\( c \)[/tex] is the length of the hypotenuse.

Here:
- [tex]\( a = 18 \)[/tex]
- [tex]\( b = 24 \)[/tex]
- [tex]\( x \)[/tex] is the hypotenuse

Thus, the equation becomes:
[tex]\[ 18^2 + 24^2 = x^2 \][/tex]

So, the correct equation to find the length of the hypotenuse [tex]\( x \)[/tex] is:
[tex]\[ 18^2 + 24^2 = x^2 \][/tex]
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