Answer:
x ≈ 6.6 cm
Step-by-step explanation:
It's a right triangle.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypoyenuse^2[/tex]
We have:
[tex]leg=13.5\ cm,\ leg=x\ cm,\ hypotenuse=(x+8.45)\ cm[/tex]
Substitute:
[tex]13.5^2+x^2=(x+8.45)^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\182.25+x^2=x^2+2(x)(8.45)+8.45^2\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\182.25=16.9x+71.4025\qquad\text{subtract 71.4025 from both sides}\\\\110.8475=16.9x\qquad\text{divide both sides by 16.9}\\\\\dfrac{110.8475}{16.9}=x\to x\approx6.6\ cm[/tex]
