a)
b
a=b-3
h=12
b^2=(\frac{1}{2}a)^2+h^2
b^2=\frac{1}{4}a^2+h^2
b^2=\frac{1}{4}(b-3)^2+h^2
b^2=\frac{1}{4}(b^2-6b+9)+12^2
b^2=\frac{1}{4}(b^2-6b+9)+144
4b^2=b^2-6b+9+576
3b^2+6b-585+0
\Delta=b^2-4ac=6^2-4*3*(-585)=36+7020=7058
\sqrt{\Delta}=84
b_1=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-6-84}{6}=\frac{-90}{6}=-15<0
b_2=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-6+84}{6}=\frac{78}{6}=13
b=13
a=b-3=13-3=10
$P=\frac{1}{2}ah=\frac{1}{2}1012=60$$cm^2$
b)
P=\frac{1}{2}bh_b
60=\frac{1}{2}*13*h_b
120=13h_b
$h_b=\frac{120}{13}=9\frac{3}{13}$$cm$