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The area of a rectangle is found by multiplying the length and the width. The length is represented by x+8 and the
width is represented by X+6. The total area is 288 in2. Solve for x in order to find the length and width of the rectangle.
State the length and width of the rectangle. Show all of your work and use complete sentences in your answer.

Respuesta :

mhanifa

Answer:

  • x = 10
  • 16 in and 18 in

Step-by-step explanation:

Area formula

  • A = wl, where w- width, l- length of rectangle

Given

  • l = x + 8
  • w = x + 6
  • A = 288 in²

As per formula

  • 288 = (x+6)*(x+8)

Solving for x

  • x² + 14x + 48 = 288
  • x² + 14x - 240 = 0
  • x= (-14 ±√14²+4*240)/2
  • x =(- 14 ± 34)/2
  • x = 10,
  • x = -24, discounted as negative

Sides of rectangle are

  • l = 10 + 8 = 18 in
  • w = 10 + 6 = 16 in
FadedElla

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GiveN:

  • Length of the rectangle = x + 8
  • Width of the rectangle = x + 6
  • Total area = 288 in²

What to find?

  • Value of x
  • Length and breadth accordingly.

Step-wise-Step Explanation:

Area of the rectangle can be calculated by Length × Breadth. We have their values, Simply plug in the formula.

⇒ Length × Breadth = 288 in²

⇒ (x + 8)(x + 6) = 288

⇒ x² + 14x + 48 - 288 = 0

⇒ x² + 14x - 240 = 0

Finding the zeroes by using middle term factorisation,

⇒ x² + 24x - 10x - 240 = 0

⇒ x(x + 24) - 10(x + 24) = 0

⇒ (x - 10)(x + 24) = 0

Then x = 10 or -24. Since the sides cannot be negative, the value of x will be 10 inches (Answer)

Sides of the rectangle:

  • Length = x + 8 = 18 in.
  • Width = x + 6 = 16 in.

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