Explicație pas cu pas:
12.
[tex]A = {l}^{2}[/tex]
[tex]A = {9}^{2} + {12}^{2} = 81 + 144 = 225 = {15}^{2}[/tex]
[tex]{l}^{2} = {15}^{2} \implies l = 15 \: cm[/tex]
13. noua arie mărită:
[tex] {(x + 4)}^{2} = 36 \iff x + 4 = 6 \\ \iff x = 6 - 4 \implies x = 2 \: cm[/tex]
[tex]P = 4l = 4 \times 2 = 8 \: cm[/tex]
14.
[tex]1 + 3 + 5 + 7 + ... + (2x - 1) = 225 \\[/tex]
[tex]1 + (1 + 2) + (1 + 4) + (1 + 6) + ... + (1 + 2x - 2) = 225 \\[/tex]
[tex](1 + 1 + 1 + 1 + ... + 1) + (2 + 4 + 8 + ... + (2(x - 1)) = 225 \\[/tex]
[tex]x + 2(1 + 2 + 3 + ... + (x - 1)) = 225 \\ [/tex]
[tex]x + 2 \cdot \frac{(x - 1)x}{2} = 225\iff x + x(x - 1) = 225 \\[/tex]
[tex]x + {x}^{2} - x = 225\iff {x}^{2} = {15}^{2} \\ [/tex]
[tex]\implies x = 15[/tex]
