Question
![In un rettangolo la base supera di 3 il quadruplo dell'altezza, che misura h+1. Trova il perimetro e l'area in funzione di h.
[10 h+16 ; 4 h^{2}+11 h+7]](https://cdn.upstudy.ai/web_qb_pics/d8fdf2286b520a253273a1182a966499?sign=%242a%2411%24B5Yu369d2Vozt7nvhMyAE.H3OKUUybdIEo6N4lLXV5LKH2KouTjv.)
In un rettangolo la base supera di 3 il quadruplo dell'altezza, che misura h+1. Trova il perimetro e l'area in funzione di h. [10 h+16 ; 4 h^{2}+11 h+7]
Ask by Rogers Mann.
Mar 22,2025 21:29
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Tutor-Verified Answer
Answer
Il perimetro del rettangolo è \( 10h + 16 \) e l'area è \( 4h^{2} + 11h + 7 \).
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Bonus Knowledge
Iniziamo a formulare le espressioni per la base e l’altezza. Se l’altezza è \( h + 1 \), la base sarà \( b = 4(h + 1) + 3 = 4h + 4 + 3 = 4h + 7 \). Ora possiamo calcolare il perimetro: \( P = 2(b + h) = 2((4h + 7) + (h + 1)) = 2(5h + 8) = 10h + 16 \).
Per l'area invece, utilizziamo \( A = base \times altezza = (4h + 7)(h + 1) = 4h^2 + 4h + 7h + 7 = 4h^2 + 11h + 7 \). Voilà! Il perimetro è \( 10h + 16 \) e l'area è \( 4h^2 + 11h + 7 \). 🍕📏
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