OG详解-OG6 数学2 Q14

The correct answer is 5. Let × represent the width, in inches, of the rectangle. It’s given that the length of the rectangle is 4 inches less than 7 times its width, or 7×-4 inches. The area of a rectangle is equal to its width multiplied by its length. Multiplying the width, × inches, by the length, 7×-4 inches, yields ×(7×-4) square inches. It’s given that the rectangle has an area of 155 square inches, so it follows that ×(7×-4) = 155, or 7ײ -4× = 155. Subtracting 155 from both sides of this equation yields 7ײ -4× - 155 = 0. Factoring the left-hand side of this equation yields (7×+31)(×-5) = 0. Applying the zero product property to this equation yields two solutions: × = - 317​​ and × = 5. Since × is the rectangle’s width, in inches,which must be positive, the value of × is 5. Therefore, the width of the rectangle, in inches, is 5.