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The area A of the rectangle shown is 500 square meters. Find the value of x. Then give the dimensions of the rectangle.

The area A of the rectangle shown is 500 square meters Find the value of x Then give the dimensions of the rectangle class=

Respuesta :

Answer:

  1. Length = 4(7) - 3 = 25 m
  2. Width = 2(7) + 6 = 20 m

Step-by-step explanation:

Area Formula

  • *Area* = *Length* × *Width*

Given

  1. Area = 500 square meters
  2. Length = (4x - 3) meters
  3. Width = (2x + 6) meters

Solving

  • (4x - 3)(2x + 6) = 500
  • 8x² - 6x + 24x - 18 = 500
  • 8x² + 18x - 18 - 500 = 0
  • 4x² + 9x - 259 = 0
  • (4x + 37)(x - 7) = 0
  • x = 7 [as distance is always positive]

Dimensions

  1. Length = 4(7) - 3 = 25 m
  2. Width = 2(7) + 6 = 20 m
  • Length=L=4x-3
  • Breadth=B=2x+6

Now

  • Area =LB
  • (4x-3)(2x+6)=500
  • 8x²+18x-518=0
  • (x-7)(4x+37)=0
  • x=7 or -37/4

Take it positive

  • L=4(7)-3=28-3=25
  • B=2(7)+6=20

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