Answer:
Dimension:
Width: x
Length: 2x + 3
Area: 560 sq. inches
Area = Length x Width
Equation:
(2x + 3) (x) = 560
2x² + 3x = 560
Transform to quadratic equation, ax² + bx + c = 0:
2x² + 3x - 560 = 0
Use Quadratic formula to solve for x:
a = 2 b = 3 c = -560
x₁,₂ = \frac{-(3) \frac{+}{-} \sqrt{(3) ^{2}-4(2)(-560) } }{2(2)}
2(2)
−(3)
−
+
(3)
2
−4(2)(−560)
x₁,₂ = \frac{-3 \frac{+}{-} \sqrt{9+4,480 } }{4}
4
−3
−
+
9+4,480
x₁,₂ = \frac{-3 \frac{+}{-} \sqrt{4489} }{4}
4
−3
−
+
4489
x₁ = \frac{-3 +67}{4}
4
−3+67
x₁ = 64/4
x₁ = 16
-------------------
x₂ = \frac{-3 -67}{4}
4
−3−67
x₂ = -70/4 or -35/2
Choose the positive root, x₁ = 16
Substitute 16 for x in dimension:
Width:x = 16 inches
Length: 2x + 3 = 2(16) + 3 = 35 inches
ANSWER: Length is 35 inches and width is 16 inches.
Check:
(35 inches) (16 inches) = 560 sq. inches
560 sq. inches = 560 sq. inches (true)
Step-by-step explanation:
i hope it helps
