Question

Ariile a patru patrate sunt direct proportionale cu numerele 25,36,64,100,iar suma perimetrelor lor este 580m.Aflati aria patratelor.Ajutor!

Answer 1

Notam
A₁/25=A₂/36=A₃/64=A₄/100
4l₁+4l₂+4l₃+4l₄=580m ⇔
4(l₁+l₂+l₃+l₄)=580m ⇔
l₁+l₂+l₃+l₄=145m
(l₁/5)²=(l₂/6)²=(l₃/8)²=(l₄/10)² ⇔
l₁/5=l₂/6=l₃/8=l₄/10=l₁+l₂+l₃+l₄ /5+6+8+10=145/29=5
l₁/5=5⇒l₁=25 ⇒A₁=625m²(aria-primul patrat);
l₂/6=5⇒l₂=30 ⇒A₂=900m²(aria-al doilea patrat);
l₃/8=5⇒l₃=40 ⇒A₃=1600m²(aria-al treilea patrat);
l₄/10=5⇒l₄=50 ⇒A₄=2500m²(aria-al patrulea patrat);