The length of a rectangular garden is 6 more than the width. Find the dimensions of the garden. The area of the garden is 120cm2

Question

The area of the rectangular garden is 120cm²

Answer 1

120 = w(w+6)

 

120 = w^2 +6w

 

0 = w^2 + 6w - 120

 

 

w = (  -6  +or-  sqrt (  36 + 4*1*120))/ 2

 

   = ( -6 +or- sqrt( 516))/2

 

  = (-6 +or- 2 * sqrt(129))/2

 

 

The negative branch results in negative measurements.

 

The width is APPROXIMATELY

(-6 + 2*sqrt(129))/2  = 8.3578167.....

  The length is 14.3578167.....

 

Answer 2

If we call length L and width W then L=W+6 (1) because the length is 6 units longer than the width. The equation for area of a rectangle says A=L*W (2). Substituting equation (1) into (2) gives A=(W+6)W=120 (3) which rearanges to W²+6W-120=0 (4) and can be solved using the quadratic formula. After discarding the negative solution, you'll find W and can find L using (1).