Question

Raportul dintre lungimea si latimea unui dreptunghi este $\frac{16}{5}$.Stiind ca perimetrul dreptunghiului este de 420 cm,sa se afle aria dreptunghiului.

Answer 1

Notam cu a si b dimensiunile dreptunghiului, a>b.

P=2(a+b)
420=2(a+b)=>a+b=210 (cm)
=> a=210-b

a/b=16/5=>
5a=16b=>
5(210-b)=16b=>
1050-5b=16b=>
1050=21b=>
b=50 (cm)

a=210-b=210-50=160 (cm)

A dreptunghi=a×b=50×160=8000 (cm^2)

Answer 2

[tex]\it \mathcal{P} = 420 \Longrightarrow 2(L+\ell) = 420|_{:2}\Longrightarrow L+\ell = 210 \ \ \ \ (*) \\\;\\ \dfrac{L}{\ell} =\dfrac{16}{5} \Longrightarrow \dfrac{L}{16} = \dfrac{\ell}{5} =\dfrac{L+\ell}{16+5} \stackrel{(*)}{=} \dfrac{210}{21} =10[/tex]

[tex]\it \dfrac{L}{16} =10 \Longrightarrow L = 16\cdot10 \Longrightarrow L = 160\ cm \\\;\\ \\\;\\ \dfrac{\ell}{5} =10 \Longrightarrow \ell = 5\cdot10 \Longrightarrow \ell = 50\ cm [/tex]


$\it \mathcal{A} = L\cdot \ell = 160\cdot50 = 8000cm^2 = 80 dm^2 = 0,8m^2$