Question

Un dreptunghi are P=28, si diag=10. Determinati aria
Dau coroana! Va rogggg!!

Answer 1

Răspuns:

48

Explicație pas cu pas:

$\mathcal{P} = 2 \cdot (L + \ell) = 28 \\ L + \ell = 14$

${d}^{2} = {L}^{2} + {\ell}^{2} \implies {L}^{2} + {\ell}^{2} = {10}^{2} \\ \iff {L}^{2} + {\ell}^{2} = 100$

${(L + \ell)}^{2} = {14}^{2}$

${L}^{2} + 2 \cdot L \cdot \ell + {\ell}^{2} = 196 \\ 100 + 2 \cdot L \cdot \ell = 196 \\ 2 \cdot L \cdot \ell = 96 \iff L \cdot \ell = 48$

$\mathcal{A} = L \cdot \ell \implies \bf \mathcal{A} = 48 \ {u.m.}^{2}$