Question

un dreptunghi are perimetrul egal cu 96 cm iar latimea sa este 3/5 din lumgimea acestuia. aria dreptunghiului este egala cu:

Answer 1

Răspuns:

P=2(L+l)

l=3L/5

96=2(⁵⁾L+3L/5)=>96:2=(5L+3L)/5=>

⁵⁾48=8L/5=>240=8l=>L=240:8=>L=30cm

l=30·3:5=>l=18cm

A=L·l

A=30·18=540 cm²

Answer 2

$\it \mathcal{P} =2\cdot(L+\ell) =96|_{:2} \Rightarrow L+\ell=48\ \ \ \ \ (1)\\ \\ \ell=\dfrac{3}{5}\ din\ L \Rightarrow \ell=\dfrac{3}{5}\cdot L|_{\cdot5}\Rightarrow5\ell=3L|_{+3\ell} \Rightarrow 8\ell=3L+3\ell \Rightarrow\\ \\ \\ \Rightarrow8\ell=3\cdot(L+\ell) \stackrel{(1)}{\Longrightarrow} 8\ell=3\cdot48|_{:8}\Rightarrow\ell=3\cdot6 \Rightarrow \ell=18\ cm\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow L+18=48 \Rightarrow L=48-18 \Rightarrow L=30\ cm\\ \\ \\ \mathcal{A} =L\cdot \ell=30\cdot18=540\ cm^2$