Question

Mario is looking for the dimensions of the rectangular garden that has an area of 14m2 and a perimeter of 18 meters.which of the following represent the given situation

Answer 1

COMPLETE QUESTION

Mario is looking for the dimensions of the rectangular garden that has an area of 14 m² and a perimeter of 18 meters.which of the following represents the given situation

$\sf{}A. \: \: \: \: {w}^{2} - 9w + 14 \: = 0\: \: \:$

$\sf{}B. \: \: \: \: {w}^{2} - 18w + 14 = 0\: \: \: \:$

$\sf{}C. \: \: \: \: {w}^{2} + 9w - 14 = 0\: \: \: \:$

$\sf{}D. \: \: \: \: {w}^{2} + 18w + 14 = 0\: \: \: \:$

SOLUTION :

Let the length and width of the rectangular garden be a metre and b metre respectively

Then

$\sf{}Perimeter \: = 2(a + b) \: \: metre$

$\sf{}Area \: = ab \: \: {metre}^{2}$

So by the given condition

$\sf{}2(a + b) = 18$

$\implies \sf{}a + b = 9 \: \: ...(1)$

Also

$\sf{}ab = 14$

Now a and b are the roots of the quadratic equation

$\sf{} {w}^{2} - (a + b)w + ab = 0$

$\implies \sf{} {w}^{2} - 9w + 14 = 0$

Hence the required answer is

$\sf{}A. \: \: \: \: {w}^{2} - 9w + 14 \: = 0\: \: \:$

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