The value of [tex]b_{1}[/tex] is 69/4h and value of [tex]b_{2}[/tex] is 43/4h if the area of trapezoid is 14 square units.
Given that area is equal to 1-2([tex]b_{1} -b_{2}[/tex])h and area is 14 square units.
We know that area of trapezoid is equal to (a+b)h/2.
We have to put the given equation equal to 14 to get our first equation.
14=1-2([tex]b_{1} -b_{2}[/tex])h
14=1-2[tex]b_{1}[/tex]h+2[tex]b_{2}[/tex]h
2[tex]b_{1}[/tex]h-2[tex]b_{2}[/tex]h=-13------------1
Now put the value of area in the formula of area of trapezoid.
14=[tex](b_{1} +b_{2})h/2[/tex]
[tex]b_{1}[/tex]h+[tex]b_{2}h[/tex]=28-----------------2
Multiply equation 2 by 2 and then subtract 2 from 1
[tex]2b_{1}h -2b_{2}h -2b_{1}h-2b_{2}h[/tex]=-13-56
-4[tex]b_{2}h[/tex]=-43
[tex]b_{2}[/tex]=43/4h
Put the value of [tex]b_{2}[/tex] in 2 to get the value of [tex]b_{1}[/tex].
[tex]b_{1} h+43/4h*h=28[/tex]
[tex]b_{1}[/tex]=69/4h
Hence The value of [tex]b_{1}[/tex] is 69/4h and value of [tex]b_{2}[/tex] is 51/4h if the area of trapezoid is 14 square units.
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