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the width of a rectangler slab of concrete is 3 m less than the length. the area is 54m^(2 )what are the dimensions of the rectangle

User Jozy
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1 Answer

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Answer:

Length = 9 m

Width = 6 m

Explanation:

The formula for the area of a rectangle is given by:

A = lw, where

  • A is the area in units squared,
  • l is the length,
  • and w is the width.

Step 1: Create an equation to model the width being 3 m less than the length:

  • Since we're told that the width is 3 m less than the length, we can model this with the following equation:

w = l - 3

Step 2: Substitute 54 for A and l - 3 for w in A = lw

Now we can plug in 54 for A and l - 3 for w in A = lw:

54 = l(l - 3)

54 = l^2 - 3l

0 = l^2 - 3l - 54

Step 3: Factor l^2 - 3l - 54 to solve the quadratic:

  • We can solve the quadratic using factoring.
  • Remember that when a variable is by itself, you can think of an imaginary 1 being in front of it.
  • Thus, l^2 is the same as saying 1 * l^2.
  • Nevertheless, we wan to find two numbers whose product is equivalent to 1 * -54 and whose sum is -3.
  • We know that 6 * -9 = -54 and 6 + (-9) = -3. Thus, our two factors are 6 and -9.

(l + 6)(l - 9) = 0

Step 4: Set both terms equal to 0 to solve for l:

Setting (l + 6) equal to 0:

l + 6 = 0

l = -6

Setting (l - 9) equal to 0:

l - 9 = 0

l = 9

Because we can't have a negative measure, l is 9 m.

Step 5: Plug in 9 for l in w = l - 3 to find w, the width:

w = 9 - 3

w = 6

Thus, the length is 9 m and the width is 6 m.

User IttayD
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