Answer:
[tex]x\approx6.5[/tex]
Step-by-step explanation:
First, we can solve for the side shared by both right triangles using the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
[tex]7^2+b^2 = 10^2[/tex]
[tex]49 + b^2 = 100[/tex]
[tex]b^2 = 100 - 49[/tex]
[tex]b^2 = 51[/tex]
[tex]b=\sqrt{51}[/tex]
Then, we can use this shared side length to solve for x, again using the Pythagorean Theorem:
[tex]a^2 + b^2 = c^2[/tex]
[tex]3^2 + x^2 = (\sqrt{51})^2[/tex]
[tex]9 + x^2 = 51[/tex]
[tex]x^2 = 51 - 9[/tex]
[tex]x^2 = 42[/tex]
[tex]x=\sqrt{42}[/tex]
Approximating using a calculator, we get:
[tex]x\approx 6.480740698[/tex]
Rounding this to the nearest tenth:
[tex]\boxed{x\approx6.5}[/tex]
