Answer:
(A) and (D)
Step-by-step explanation:
It is given that the given expression [tex]a=\frac{1}{2}(b_{1}+b_{2})h[/tex]can be used to determine the area, a, of a trapezoid with height, h, and base lengths [tex]b_{1}[/tex] and [tex]b_{1}[/tex].
Thus, solving the given equation and finding the value of [tex]b_{1}[/tex], we get
[tex]a=\frac{1}{2}(b_{1}+b_{2})h[/tex]
[tex]\frac{2a}{h}-b_{2}=b_{1}[/tex]
And the expression for height is:
[tex]2a=(b_{1}+b_{2})h[/tex]
[tex]h=\frac{2a}{(b_{1}+b_{2})}[/tex]
(A) The given expression is:
[tex]\frac{2a}{h}-b_{2}=b_{1}[/tex]
which is equivalent to the given expression, therefore this option is correct.
(B) The given expression is:
[tex]\frac{a}{2h}-b_{2}=b_{1}[/tex]
which is not equivalent to the given expression, therefore this option is not correct.
(C) The given expression is:
[tex]\frac{2a-b_{2}}{h}=b_{1}[/tex]
which is not equivalent to the given expression, therefore this option is not correct.
(D) The given expression is:
[tex]\frac{2a}{b_{1}+b_{2}}=h[/tex]
which is equivalent to the given expression, therefore this option is correct.
(E) The given expression is:
[tex]\frac{a}{2(b_{1}+b_{2})}=h[/tex]
which is not equivalent to the given expression, therefore this option is not correct.
