Answer:
12.1 inches
Step-by-step explanation:
Since the length of the rectangular painting is (2x + 5) inches and its width is x inches, it area A = (2x + 5)x square inches = 2x² + 5x.
Also, A = 420 square inches. So,
2x² + 5x = 420
2x² + 5x - 420 = 0
diving through by 2, we have
2x²/2 + 5x/2 - 420/2 = 0/2
x² + 5x/2 - 210 = 0
adding halt the coefficient of x squared to both sides, that is (5/2 ÷ 2)² = (5/4)² to both sides, we have
x² + 5x/2 + (5/4)² - 210 = 0 + (5/4)²
Simplifying, we have
(x + 5/2)² - 210 = 25/16
adding 210 to both sides, we have
(x + 5/2)² - 210 + 210 = 25/16 + 210
(x + 5/2)² = 25/16 + 210
(x + 5/2)² = (25 + 3360)/16
(x + 5/2)² = 3385/16
taking square root of both sides, we have
√(x + 5/2)² = ±√(3385/16)
(x + 5/2) = ±√3385/4
(x + 5/2) = ±58.18075/4
(x + 5/2) = ±14.55
x = -5/2 ±14.55
x = -2.5 ±14.55
x = -2.5 - 14.55 or -2.5 + 14.55
x = - 17.05 or 12.05
Since x = width and it cannot be negative, we choose the positive answer. So, x = 12.05 inches ≅ 12.1 inches (to the nearest tenth)
