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Lorena's garden is surrounded by a corridor of uniform width. The garden and the hallway together cover an area of 320 square meters. If the garden measures 12 meters by 16 meters. determines the width of the hallway

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Answer to a math question Lorena's garden is surrounded by a corridor of uniform width. The garden and the hallway together cover an area of 320 square meters. If the garden measures 12 meters by 16 meters. determines the width of the hallway

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Eliseo
4.6
109 Answers
A continuación se explica cómo resolver el problema: **1. Encuentra el área del jardín:** * Área del jardín = largo * ancho * Área de jardín = 12 metros * 16 metros = 192 metros cuadrados **2. Encuentra el área total del jardín y el pasillo:** * El jardín y el pasillo combinados tienen una superficie de 320 metros cuadrados. **3. Encuentra el área del pasillo:** * Área del pasillo = Área total - Área del jardín * Área del pasillo = 320 metros cuadrados - 192 metros cuadrados = 128 metros cuadrados **4. Modela el pasillo:** * Imagine el pasillo como un marco alrededor del jardín. Llamemos al ancho del pasillo "x". * El largo del jardín más el doble del ancho del pasillo sería 12 + 2x. * El ancho del jardín más el doble del ancho del pasillo sería 16 + 2x. **5. Establecer una ecuación** * El área del pasillo es igual al área total menos el área del jardín: (12 + 2x)(16 + 2x) - 192 = 128 **6. Resuelve la ecuación:** * Ampliar la ecuación: 192 + 56x + 4x^2 - 192 = 128 * Simplificar: 4x^2 + 56x - 128 = 0 *Dividir ambos lados entre 4: x^2 + 14x - 32 = 0 * Factorizar: (x + 16)(x - 2) = 0 *Resolver para x: x = -16 o x = 2 **7. Elija la solución positiva:** *El ancho del pasillo no puede ser negativo, por lo que el ancho del pasillo es de 2 metros. **Respuesta:** El pasillo tiene un ancho de 2 metros.

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