Question

Care este aria unui romb știind ca suma diagonalelor este 96 iar una este 5/3 din cealaltă?

Answer 1

$d_{1} + d_{2} = 96$

$d_{1} = \frac{5}{3} \times d_{2} = \frac{5d_{2}}{3}$

$\frac{5d_{2}}{3} + d_{2} = 96 \: | \times 3$

$5d_{2} + 3d_{2} = 288$

$8d_{2} = 288 \: | \div 8$

$d_{2} = 36$

$d_{1} = \frac{5d_{2}}{3} = \frac{5 \times 36}{3} = 5 \times 12 = 60$

$A=\frac{d_{1} \: \times \: d_{2}}{2} = \frac{60 \times 36}{2} = 60 \times 18 = 1080$

Answer 2

A=d×D/2
d+D=96
D/d=5/3
D/5=d/3=k
D=5k
d=3k
5k+3k=96
8k=96
k=12
D=60u
d=36u
u unitati
A=36×60/2
A=2160/2
A=1080u^2