Answer:
x = 6.5 cm
Step-by-step explanation:
The segment 20.2 cm is the tangent. Therefore x and 20.2cm are perpendicular.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=x,\ leg=20.2cm,\ hypotenuse=(14.7+x)cm[/tex]
Substitute:
[tex]x^2+20.2^2=(14.7+x)^2[/tex] use (a + b)² = a² + 2ab + b²
[tex]x^2+408.04=14.7^2+(2)(14.7)(x)+x^2[/tex] subtract x² from both sides
[tex]408.04=216.09+29.4x[/tex] subtract 216.09 from both sides
[tex]191.95=29.4x[/tex] divide both sides by 29.4
[tex]x\approx6.5\ cm[/tex]
