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The width of a rectangle is 5 inches less than twice the length. The area of the rectangle is 700 square inches. Which equation could be used to determine the length of the rectangle? A x2 - 5x = 700 B 2x2 - 5x - 700 = 0 C 2x2 - 5x + 700 = 0 D 2x2 + 5x = 700

Respuesta :

altavistard
width:     W = 2L-5
area:      A = 700 sq in

A=L*W, so L = A/W.  Thus, L = (700 sq in) / (2L - 5 in)

Solve this for L.  Mult both sides of this equation by (2L-5), obtaining

L(2L-5) = 700.  Then, 2L^2 - 5L - 700 = 0

Using the quadratic formula to solve for L:

        -(-5) plus or minus sqrt( [-5]^2 - 4[2][-700] )
L = ------------------------------------------------------------
                             2[2]
             
           5 plus or minus sqrt(25+5600)
    = ----------------------------------------------
                                4
        5 plus or minus sqrt(5625)       5 plus or minus 75
    = ------------------------------------- = ---------------------------
                                  4                                   4

     = 20 or -17.5.  choose the positive result.  Thus, L = 20 inches, and 
                                                                      W = 2(20 in) - 5 in = 35 inches.