Question 110788
A rectangle flower garden, 7m by 6 m, is surrounded by a grass strip of uniform width. If the total area of the garden and the grass strip is 90m, what is the width of the strip?

Given:
{{{Length = L = 7m }}}

{{{Width = W = 6 m}}}

{{{total_ area = A[3]  = 90m^2}}}

Then:

{{{total_ area  = are_of_rectangle  -plus_ a_ grass_ strip _ area= A}}} }}}

{{{A = (7+ G)(6 + G)}}}

0r	
{{{90= (7+ G)(6 + G)}}}

{{{ 90= 42 + 7G + 6G + G^2 }}}

{{{ 90=  42 + 13G  + G^2 }}}

{{{ G^2 + 13G  + 42 – 90 = 0}}}

{{{ G^2 + 13G   – 48 = 0}}}

Solve for {{{G}}} using quadratic formula:

{{{ G[1,2] =(-b +- sqrt (b^2 -4*a*c )) / (2*a)}}}

{{{ G[1,2] =(-13 +- sqrt (13^2 - 4*1*(-48) )) / (2*1)}}}

{{{ G[1,2] =(-13 +- sqrt (169 +  192)) / (2)}}}

{{{ G[1,2] =(-13 +- sqrt (361)) / (2)}}}

{{{ G[1,2] =(-13 +- 19) / (2)}}}

We need only positive root:

{{{ G[1,2] =(-13 + 19) / 2}}}

{{{ G[1,2] = 6 / 2}}}

{{{ G[1,2] = 3m}}}

Check:

{{{90m^2= (7m+ Gm)(6m + Gm)}}}

{{{90m^2= (7m + 3m)(6m + 3m)}}}

{{{90m^2= 10m*9m}}}

{{{90m^2= 90m^2}}}