Question

This is my third time asking this and no answer, i need to get this done today. i will give brainliest.

Answer 1

Answer:

  29 by 70 meters

Step-by-step explanation:

You need to know how area and perimeter relate to the dimensions of the lawn.

The area formula is ...

  A = LW . . . . . . . the product of length and width

The perimeter formula is ...

  P = 2(L+W) . . . . twice the sum of length and width

The latter tells you the sum of length and width will be ...

  P/2 = L + W = (198 m)/2 = 99 m

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It usually works well to assume that the dimensions are integers, then look for the factors of the area figure that give the right perimeter.

  2030 = 2·5·7·29

  = 2×1015 = 5×406 = 7×290 = 10×203 = 14×145 = 29×70 = 35×58

Of these factor pairs, the one that has a sum of 99 is (29, 70).

The dimensions of the lawn are 29 m by 70 m.

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You can also solve this graphically or algebraically. The graphical solution finds the points of intersection between LW=2030 and L+W=99, or the equivalent. Attached is a graph of the problem.

The algebraic solution can use substitution:

  L = 99-W

  2030 = (99 -W)(W)

  W² -99W +2030 = 0 . . . . subtract the right side and put in standard form

  W = (99±√(99² -4·2030))/2 . . . . . . use the quadratic formula

  W = (99 +√1681)/2 = (99 ±41)/2 = {29, 70}

It doesn't matter which dimension you call the width.

The lawn is 29 m by 70 m.

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The quadratic formula tells you the solution to ...

  $ax^2+bx+c=0$

is given by ...

  $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, we have a=1, b=-99, c=2030.

Of course (-99)² = 99², and 4(1)(2030) = 4·2030, so we have simplified the solution a little bit when writing it above.