Question

The length of a rectangle is 5 centimeters less than three times its width. Its area is 28 square centimeters. Find the dimensions of the rectangle.

Answer 1

Answer:

  4 cm by 7 cm

Step-by-step explanation:

The relation between length and width can be used with the area formula to find the dimensions of the rectangle.

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setup

Let x represent the width of the rectangle. Then the length is (3x-5). The area is the product of length and width.

  A = LW

  28 = (3x -5)(x)

In standard form, this is ...

  3x² -5x -28 = 0

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solution

factor

To factor this equation, we are looking for factors of (3)(-28) = -84 that have a total of -5. The factor pairs of -84 are ...

  -84 = -84×1 = -42×2 = -28×3 = -21×4 = -14×6 = -12×7

Sums of these pairs are -83, -40, -25, -17, -8, -5.

The last pair, -12×7, gives us a clue as to how to factor the equation.

  3x² -5x -28 = (3x -12)(3x +7)/3 = (x -4)(3x +7)

Then the equation we want a solution for is ...

  (x -4)(3x +7) = 0

zero product rule

The only positive value of x that makes either factor zero is ...

  x = 4

And the other dimension is ...

  3x -5 = 3(4) -5 = 7

The rectangle is 5 cm wide and 7 cm long.