To find the value of [tex]\( x \)[/tex] in the equation [tex]\( 3.5^2 + x^2 = 5.6^2 \)[/tex], we will follow these steps:
1. Square the known values [tex]\( 3.5 \)[/tex] and [tex]\( 5.6 \)[/tex]:
[tex]\[
3.5^2 = 3.5 \times 3.5 = 12.25
\][/tex]
[tex]\[
5.6^2 = 5.6 \times 5.6 = 31.36
\][/tex]
2. Substitute these squares into the original equation:
[tex]\[
12.25 + x^2 = 31.36
\][/tex]
3. Rearrange the equation to solve for [tex]\( x^2 \)[/tex]:
[tex]\[
x^2 = 31.36 - 12.25
\][/tex]
4. Subtract the squares:
[tex]\[
x^2 = 31.36 - 12.25 = 19.11
\][/tex]
5. Take the square root of both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \sqrt{19.11}
\][/tex]
6. Calculate the square root and round to the nearest hundredth:
[tex]\[
x \approx 4.37
\][/tex]
So, the value of [tex]\( x \)[/tex] rounded to the nearest hundredth is [tex]\( 4.37 \)[/tex].
