Mathematic Problems
347. példa

Calculate the area of the Isosceles triangle if the base height is 20 cm and the arm height is 24 cm.

$a·{h}_{a}=b·{h}_{b}$
$a·20=b·24$
$b=\frac{a·20}{24}=\frac{5·a}{6}$
${b}^{2}={\left(\frac{a}{2}\right)}^{2}+{h}_{b}^{2}$
${\left(\frac{5a}{6}\right)}^{2}={\left(\frac{a}{2}\right)}^{2}+{20}^{2}$
$\frac{25{a}^{2}}{36}=\frac{{a}^{2}}{4}+400{|}{·}{36}$
$25{a}^{2}=9{a}^{2}+14400$
$16{a}^{2}=14400$
${a}^{2}=\frac{14400}{16}=900$
$a=\sqrt{900}=30$
$T=\frac{a·{h}_{a}}{2}=\frac{30·20}{2}$