Answer :
Answer:
Area of the rectangle = -(x - 15/2)² + 49/4
Step-by-step explanation:
* Lets revise the rule of the area of the rectangle
- Any rectangle has two dimensions,length and width
-The area of the rectangle = length × width
* In our problem the dimensions of the rectangle are
(11 - x) and (x - 4)
∴ The area of the rectangle = (11 - x)(x - 4)
- Lets multiply the two brackets
∴ (11 - x)(x - 4) = 11 × x + 11 × (-4) + (-x) × (x) + (-x) × (-4)
∴ (11 - x)(x - 4) = 11x - 44 - x² + 4x ⇒ collect the like terms
∴ (11 - x)(x - 4) = -x² + 15x - 44
* The area of the rectangle = -x² + 15x - 44
- To put them in the standard form a(x + h)² + k, lets equate
the two forms to find a , h and k
∵ -x² + 15x - 44 = a(x + h)² + k
∴ -x² + 15x - 44 = a(x² + 2hx + h²) + k
∴ -x² + 15x - 44 = ax² + 2ahx +ah² + k
* Compare the two sides
∵ -1 = a ⇒ coefficient of x²
∴ a = -1
∵ 2ah = 15 ⇒ coefficient of x
∴ 2(-1)h = 15 ⇒ -2h = 15 ⇒ divide the both sides by -2
∴ h = -15/2 = -7.5
∵ ah² + k = -44
∴ (-1)(-15/2)² + k = -44
∴ -225/4 + k = -44 ⇒ add -225/4 to the both sides
∴ k = 49/4 = 12.25
* The standard form of the equation is -(x - 15/2)² + 49/4
∴ The quadratic equation represented the area is
A = -(x - 15/2)² + 49/4
Answer:
Step-by-step explanation:
the area is : (1-x)(x-4) m² and (1 - x > 0 and x - 4 > 0 )
(1-x)(x-4) = x - 4 - x²+4x
(1-x)(x-4) = - x² +5x - 4 ..... quadratic equation in standard form