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mixas84 [53]
4 years ago
13

Please help. I don’t understand this and it’s due tomorrow. Thx

Mathematics
1 answer:
Rama09 [41]4 years ago
6 0

a.\: Area \:  of  \: carpet: 24 \times 30 = 720 \:  {ft}^{2}  \\ Area \:  of  \:border:720 - 432 = 288 \:  {ft}^{2}  \\ Equation:60x + 2x(24 - 2x) = 288 \: (0 < x < 24) \\  \\ b. \: 60x + 2x(24 - 2x) = 288 \\ \Leftrightarrow  - 4 {x}^{2}  + 48x + 60x = 288 \\ \Leftrightarrow  - 4 {x}^{2}  + 108x - 288 = 0 \\ \Leftrightarrow  {x}^{2}   - 27x + 72 = 0 \\ \Leftrightarrow  {x}^{2}  - 3x - 24x + 72 = 0 \\ \Leftrightarrow x(x  - 3) - 24(x - 3) = 0 \\ \Leftrightarrow (x - 24)(x - 3) = 0 \\ \Leftrightarrow x - 24 = 0 \: \vee \: x - 3 = 0 \\ \Leftrightarrow x = 24  \: \vee \:x = 3 \\ \Rightarrow x = 3 \: (0 < x < 24) \\ \Rightarrow The \:  width \:  of \:  the \:  border  \: is  \: 3 \:  ft

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