Answer :
To determine the correct equation to solve for [tex]\( x \)[/tex], let's evaluate each given equation step-by-step:
### Option (a)
[tex]\[ 5^2 + 12.1^2 = x^2 \][/tex]
This equation is a variation of the Pythagorean theorem, which states that in a right-angled triangle, the sum of the squares of the two legs equals the square of the hypotenuse. Here, [tex]\( 5 \)[/tex] and [tex]\( 12.1 \)[/tex] are the legs, and [tex]\( x \)[/tex] is the hypotenuse.
### Option (b)
[tex]\[ x = 15.5 + 12.1 \][/tex]
This equation simply sums two numbers. It does not involve squaring or relate to the Pythagorean theorem at all.
### Option (c)
[tex]\[ 15.5^2 - 12.1^2 = x^2 \][/tex]
This equation looks similar to the difference of squares identity, which does not align with the Pythagorean theorem setup we are dealing with.
### Option (d)
[tex]\[ x^2 + 15.5^2 = 12.1^2 \][/tex]
This equation suggests that the sum of the square of [tex]\( x \)[/tex] and the square of [tex]\( 15.5 \)[/tex] equals the square of [tex]\( 12.1 \)[/tex]. This does not match the original problem statement either.
Given these evaluations, the correct equation to solve for [tex]\( x \)[/tex] in the context of the Pythagorean theorem is:
[tex]\[ 5^2 + 12.1^2 = x^2 \][/tex]
### Option (a)
[tex]\[ 5^2 + 12.1^2 = x^2 \][/tex]
This equation is a variation of the Pythagorean theorem, which states that in a right-angled triangle, the sum of the squares of the two legs equals the square of the hypotenuse. Here, [tex]\( 5 \)[/tex] and [tex]\( 12.1 \)[/tex] are the legs, and [tex]\( x \)[/tex] is the hypotenuse.
### Option (b)
[tex]\[ x = 15.5 + 12.1 \][/tex]
This equation simply sums two numbers. It does not involve squaring or relate to the Pythagorean theorem at all.
### Option (c)
[tex]\[ 15.5^2 - 12.1^2 = x^2 \][/tex]
This equation looks similar to the difference of squares identity, which does not align with the Pythagorean theorem setup we are dealing with.
### Option (d)
[tex]\[ x^2 + 15.5^2 = 12.1^2 \][/tex]
This equation suggests that the sum of the square of [tex]\( x \)[/tex] and the square of [tex]\( 15.5 \)[/tex] equals the square of [tex]\( 12.1 \)[/tex]. This does not match the original problem statement either.
Given these evaluations, the correct equation to solve for [tex]\( x \)[/tex] in the context of the Pythagorean theorem is:
[tex]\[ 5^2 + 12.1^2 = x^2 \][/tex]
