Question

question solve for x to the nearest tenth.

Explanation:

Step1: Find the length of the hypotenuse of the lower - right triangle

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$ for the right - triangle with sides 7 and 10. Let the hypotenuse be $h$. Then $h=\sqrt{7^{2}+10^{2}}=\sqrt{49 + 100}=\sqrt{149}$.

Step2: Use the Pythagorean theorem for the upper - left triangle

For the right - triangle with sides 4 and $x$ and the hypotenuse equal to the $h$ we just found. So $4^{2}+x^{2}=h^{2}$. Since $h^{2}=149$, we have $16+x^{2}=149$.

Step3: Solve for $x$

Subtract 16 from both sides: $x^{2}=149 - 16=133$. Then $x=\sqrt{133}\approx11.5$.

Answer:

$11.5$