Question

A rectangular field measures 20 m by 30 m. The farmer will increase the size of the field by increasing each side length by the same amount. The resulting enclosed area of the field is to be 1064 m2 . Find the dimensions of the new field (to the nearest tenth, if necessary).

Answer 1

Answer:

28m by 38 m

Step-by-step explanation:

A = lw

l = 20 + x

w = 30 + x

(20 + x)(30 + x) = 1064

x² + 50x + 600 = 1064

x² + 50x + 600 - 1064 = 0

x² + 50x - 464 = 0

D = 2500 + 1856 = 4356

$x_{12}$ = (- 50 ± √4356) / 2

$x_{1}$ = (- 50 + 66) / 2 = 8

$x_{2}$ = (- 50 - 66) / 2 = - 58 ( distance cannot be negative)

l = 28 m

w = 38 m

Answer 2

Given :    A rectangular field measures 20 m by 30 m.  each side length increased by the same amount resulted in  area of the field is to be 1064m²

To find : dimensions of the new field  

Solution:

A rectangular field measures 20 m by 30 m.

=> Area  = 20 * 30 =  600 m²

Let say each side is increased by x  m

Then new Dimensions = 20 + x  , 30 + x m

New Area = (20 + x)(30 + x)   = 1064

=> 600 + 50x + x ² = 1064

=> x²  + 50x  - 464 = 0

=> x² + 58x - 8x - 464 = 0

=> x(x + 58) - 8(x + 58) = 0

=> (x - 8)(x + 58) = 0

=> x = 8

Each sides increased by 8 m

the dimensions of the new field  = 28 m  &  38 m

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