The diagonal of a rectangular field is 60 meters more than the shorter side.If the longer side is 30 meters more than the shorter side,find the side of the field.
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Answer:
sides l=120 m and b= 90 m
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Given:-
- The diagonal of a rectangular field is 60 meters
- The longer side is 30 meter.
To find:-
- Find the side of the field.?
Solutions:-
- Let the shorter side of the rectangle be x m.
Then,
Larger side of the rectangle = (x + 30)m
Diagonal of the rectangle = √x² + (x + 30)²
The diagonal of the rectangle is 60 m more that the shorter side.
Therefore,
=> √x² + (x + 30)² = x + 60
=> x² + (x + 30)² = (x + 60)²
=> x² + x² + 900 + 60x = x² + 3600 + 120x
=> x² - 60x - 2700 = 0
=> x² - 90x + 30x - 2700 = 0
=> x(x - 90) + 30(x + 90) = 0
=> (x - 90) (x + 30) = 0
=> x - 90 = 0 or x + 30 = 0
=> x = 90 or x = - 30
- Side cannot be negative
Therefore,
The length of the shorts side be 90m
length of the larger side be (90 + 30) = 120m
Hence, the side of the field is 120m.
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