Question

A picture is 6 inches longer than it is wide and has an area of 167 square inches. What are the dimensions (in inches) of the picture. Round your answers to two decimal places.

Answer 1

Explanation:

Let x = width.

Length = x + 6.

area = length × width

area = (x + 6)x = x² + 6x

area = 167

x² + 6x = 167

x² + 6x - 167 = 0

x = [-b ± √(b² - 4ac)]/(2a)

x = [-6 ± √(6² - 4(1)(-167))]/[2(1)]

x = [-6 ± √(36 + 668)]/2

x = [-6 ± √(704)]/2

x = -3 ± [√(64 × 11)]/2

x = -3 ± 4√(11)

x = 10.27; the other value of x is negative and is discarded since a width must be positive

x + 6 = 16.27

Answer: length 16.27 inches; width 10.27 inches