Answer:
[tex]b_{2}=\frac{2A}{h}-b_{1}[/tex]
Step-by-step explanation:
Area of Trapezoid is given by:
[tex]A=\frac{1}{2}(b_{1}+b_{2})h[/tex]
Using distributive property [ [tex]a(b+c)=ab+ac[/tex] ] and simplifying:
[tex]A=\frac{1}{2}hb_{1}+\frac{1}{2}hb_{2}[/tex]
Now, doing some algebra and solving for [tex]b_{2}[/tex] gives us:
[tex]A-\frac{1}{2}hb_{1}=\frac{1}{2}hb_{2}\\\frac{A-\frac{1}{2}hb_{1}}{\frac{1}{2}h}=b_{2}\\\frac{A}{\frac{h}{2}}-\frac{\frac{1}{2}hb_{1}}{\frac{1}{2}h}=b_{2}\\\frac{2A}{h}-b_{1}=b_{2}[/tex]
This is our answer.
