Question

Use the given area A of the rectangle to find the value of x . A rectangle with its length labeled left-parenthesis 4 x plus 3 right-parenthesis feet and width labeled left-parenthesis 4 x minus 5 right-parenthesis feet. The area of the rectangle is 209 square feet.

Answer 1

x = 4

Explanation:

Length = (4x + 3) feet

Width = (4x - 5 )feet

Area = Length x Breadth

209 = (4x + 3)(4x - 5)

209 = 4x( 4x -5) + 3 (4x -5)

`209 = 16x^2 -20x +12x -15\\\\0 = 16x^2 -8x -15 -209\\\\16x^2 -8x -224 = 0`

`Quadratic \ Equation \ with a = 16, b = -8, c = -224 \\\\x = (-b \pm √(b^2 -4ac))/(2a)\\\\Substitute \ a, b, c \ in \ the \ equation.\\\\x = (-b + √(b^2 -4ac))/(2a), x =(-b \ - √(b^2 -4ac))/(2a)\\\\x = (8+ √(64 +14336))/(32), x = (8- √(64 +14336))/(32)\\\\x = (8+ √(14400))/(32), x = (8-√(14400))/(32)\\\\x = (8+120 )/(32), x= (8-120)/(32)\\\\x = (128)/(32) , x = (-112)/(32)\\\\x = 4 , x = (-7)/(2)`

Since measure of length or width cannot be negative, we take x = 4