Question

Se considera patratul ABCD in care AC∩BD={O}. Daca BO=√10cm, sa se afle aria patratului ABCD.

Answer 1

BO=DO=AO=CO=AC/2=BD/2 (ABCD patrat)=>
AC=2BO
AC=2√10
In orice patrat diagonala este egala cu latura×√2=>
AC=AB√2=>
2√10=AB√2=>
√(10×4)=AB√2=>
√40=AB√2=>
AB=√20=2√5. (cm)

A patrat=AB^2=2√5×2√5=>
A patrat=4√25=4×5=20 (cm^2)