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A livestock pen is built in the shape of a rectangle that is 3 times as long as it is wide. The perimeter is 56 feet. If the material used to build the pen is $1.50 per foot for the longer sides and $2.75 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen.

Respuesta :

adioabiola

The cost of the shorter and longer side of the rectangular pen is $19.25 and $31.50 respectively.

Perimeter of rectangle

  • Width = x
  • Length = 3x
  • Perimeter = 56 feet

Perimeter = 2(length + width)

56 = 2(3x + x)

56 = 2(4x)

56 = 8x

x = 56/8

x = 7

So,

Width = x

= 7 feet

Length = 3x

= 3(7)

= 21 feet

Cost of material used for the shorter side = $2.75 × 7

= $19.25

Cost of material used for the longer side = $1.50 × 21

= $31.50

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