Question

Ariile a patru patrate sunt invers proportionale cu numerele 1/4,1/25,1/64,1/100 iar suma  dinte cel mai mic si cel mai mare perimetru  este 48 cm .Aflati lungimile laturilor celor patru patrate

Answer 1

Notez cu a,b,c si d lungimile laturilor celor patru patrate. Atunci ariile vor fi a², b², c² si, respectiv d².

4a+4d=48 <=> 4(a+d)=48 => a+d=12.

$a^{2} * \frac{1}{4}= b^{2} * \frac{1}{25}= c^{2} * \frac{1}{64}= d^{2} *\frac{1}{100} <=> \\ <=> \frac{ a^{2} }{4}= \frac{ b^{2} }{25} = \frac{ c^{2} }{64}= \frac{ d^{2} }{100}=> \\ =>| \frac{ a }{2}|= |\frac{b}{5} | = |\frac{c}{8}|=| \frac{d}{10}| <=>\\ <=> \frac{a}{2} = \frac{b}{5} = \frac{c}{8}= \frac{d}{10} = \frac{a+d}{2+10}= \frac{48}{12}=4. \\ \\ \frac{a}{2}=4=>a=8(cm) \\ \frac{b}{5}=4=>b=20 (cm) \\ \frac{c}{8} =4=>c=32(cm) \\ \frac{d}{10}=8=>d=80(cm)$