a)
[tex]P=\dfrac{e\cdot f}2\qquad/\cdot2\\\\2P=e\cdot f\qquad/:e\\\\\dfrac{2P}e=f\\\\f=\dfrac{2P}e[/tex]
b)
[tex]V=\frac13ab\cdot H\qquad/\cdot3\\\\3V=ab\cdot H\qquad/:(ab)\\\\\dfrac{3V}{ab}=H\\\\H=\dfrac{3V}{ab}[/tex]
c)
[tex]P=\dfrac{(a+b)h}2\qquad/\cdot2\\\\2P=(a+b)h\qquad/:h\\\\\dfrac{2P}h=a+b\qquad/-a\\\\\dfrac{2P}h-a=b\\\\b=\dfrac{2P}h-a[/tex]
d)
[tex]d=a\sqrt2\qquad/:\sqrt2\\\\\dfrac{d}{\sqrt2}=a\\\\a=\dfrac{d}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}\\\\a=\dfrac{d\sqrt2}2[/tex]
e)
[tex]h=\dfrac{a\sqrt3}2\qquad/\cdot2\\\\2h=a\sqrt3\qquad/:\sqrt3\\\\\dfrac{2h}{\sqrt3}=a\\\\a=\dfrac{2h}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}\\\\a=\dfrac{2h\sqrt3}3[/tex]
f)
[tex]P=\dfrac{r(a+b+c)}2\qquad/\cdot2\\\\2P=r(a+b+c)\qquad/:r\\\\\dfrac{2P}r=a+b+c\qquad/-b\\\\\dfrac{2P}r-b=a+c\qquad/-c\\\\\dfrac{2P}r-b-c=a\\\\a=\dfrac{2P}r-b-c[/tex]
