Question

1.Calculati perimetrul si aria dreptunghiului ABCD daca A(√2, 7); B(5√2, 0) si C(3√2, √17).
2. Aflati perimetrul ΔABC daca A(2√3,1); B(0,3); C(3√3, 6).

Answer 1

se foloseste formula AB=√(x₁-x₂)²+(y₁-y₂)²
 unde 
x₁, y₁= coordonatele lui A
x₂, y₂ = coordonatele lui B

1)
A(√2, 7);
B(5√2, 0)
C(3√2, √17)
AB=√[(√2-5√2)²+(7-0)²]=√(32+49)=√81=9
BC=√[(5√2-3√2)²+(0-√17)²]=√(8+17)=√25=5
P=2×(9+5)=28 cm
A=9×5=45 cm²

2)
A(2√3,1)
B(0,3)
C(3√3, 6)

AB=√[(2√3-0)²+(1-3)²]=√(12+4)=√16=4
AC=√[(2√3-3√3)²+(1-6)²]=√(3+25)=√28=2√7
BC=√[(0-3√3)²+(3-6)²]=√(27+9)=√36=6
P=4+6+2√7=10+2√7