Question

What is the value of x? Round to the nearest tenth. Please Help

Answer 1

x = 6.5 cm

Explanation:

The segment 20.2 cm is the tangent. Therefore x and 20.2cm are perpendicular.

Use the Pythagorean theorem:

`leg^2+leg^2=hypotenuse^2`

We have

`leg=x,\ leg=20.2cm,\ hypotenuse=(14.7+x)cm`

Substitute:

`x^2+20.2^2=(14.7+x)^2` use (a + b)² = a² + 2ab + b²

`x^2+408.04=14.7^2+(2)(14.7)(x)+x^2` subtract x² from both sides

`408.04=216.09+29.4x` subtract 216.09 from both sides

`191.95=29.4x` divide both sides by 29.4

`x\approx6.5\ cm`