Question

Un rectángulo tiene 24m de perímetro y 35m2 de área. Hallar las dimensiones. , .

Answer 1

Day,
Vamos paso a paso

         DIMENSIONES RECTÁNGULO
                   LARGO = L
                   ANCHO = A
                        L > A

         PERÍMETRO = P                                 AREA = S
                                P = 2(L + A)                             S = LxA
                              24 = 2(L + A)                             35 = LxA  (2)
                               12 = L + A    (1)

                                          De (1)
                                                   L = 12 - A   (3)
                                          (3) en (2)
                                                   35 = (12 - A)xA
                                         Efectuando
                                                    35 = 12A - A^2
                                         Ordenando ecuación
                                                    A^2 - 12A + 35 = 0
                                         Resolviendo por factorización
                                                    (A - 7)(A - 5) = 0
                                                             A - 7 = 0
                                                                              A1 = 7
                                                             A - 5 = 0
                                                                              A2 = 5
                          A es la menor de las medidas
                                               A = 5
                          A en (1)
                                             12 = L + 5
                                        12 - 5 = L
                                               L = 7
                                                             DIMENSIONES
                                                                 LARGO = 7 m
                                                                 ANCHO = 5 m