Word Problem

Question

A rectangle has dimensions (2x + 5) and (3x - 2) and an area of 130 units squared. Determine the value of x.

Answer 1

Area of rectangle = l*w

 

    (2x+5)*(3x-2) = 130

    6x² -4x +15x - 10 = 130 [use F-O-I-L]

    6x² + 11x -140 = 0

    (6x + 35)(x - 4)  = 0      [either factor or use quadratic formula]

Either x=-35 or x=4              [Multiplicative Property of Zero]

    Not x=-35, negative length

 

    x = 4

 

Check:

    Rectangle is:

        2x+5 = 13

        3x-2 = 10

    Area = 130 square units