Question Number 104235 by bemath last updated on 20/Jul/20
$${If}\:{you}\:{are}\:{given}\:{a}\:{triangle} \\ $$$${with}\:{side}\:{length}\:\mathrm{15}\:,\:\mathrm{20}\:{and} \\ $$$$\mathrm{25}.\:{what}\:{is}\:{the}\:{triangle}'{s} \\ $$$${shortest}\:{altitude}? \\ $$
Answered by nimnim last updated on 20/Jul/20
$$\left(\mathrm{15},\mathrm{20},\mathrm{25}\right)\:{is}\:{a}\:{Pythagorean}\:{triple}. \\ $$$$\:\:{then}\:\:{area}\left(\bigtriangleup\right)=\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{15}×\mathrm{20}=\mathrm{150} \\ $$$$\therefore\:{Shortest}\:{alt}.=\frac{\mathrm{2}×\left(\bigtriangleup\right)}{{longest}\:{side}}=\frac{\mathrm{2}×\mathrm{150}}{\mathrm{25}}=\mathrm{12}\:{units}. \\ $$$$ \\ $$