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 1064m ^. Find the dimensions of the new field (to the nearest tenth, if necessary).
Answers
New Dimensions will be:
Length = 38m
Breadth = 28m
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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