The perimeter of a triangular plot of land is 2400ft. The longest side is 200 ft less than twice the shortest. The middle side is is 200 ft ,ess than the longest side. Finde the lengths of the three sides of the triangular plot

fortdefruitI 2020-12-31 Answered
The perimeter of a triangular plot of land is 2400ft. The longest side is 200 ft less than twice the shortest. The middle side is is 200 ft ,ess than the longest side. Finde the lengths of the three sides of the triangular plot
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Aamina Herring
Answered 2021-01-01 Author has 85 answers
a, b and c be the shortest, middle and longest sides of the triangle respectively.
Then according to given data, we get
a+b+c=2400(1)[:Perimeter = sum of all sides]
c=2a200(2) [logest side is 200 feet less than whe twice the shortest]
b=c200(3) [middle side is 200 feet less than the logest side]
From equation (1), we have
a=2400bc
equation (2) becomes,
c=2(2400bc)200c=48002b2c200
3c=46002b3c=46002b3c=46002(c200) [using equation (3)]
3c=46002c+4005c=5000c=1000
Now substituting c=1000 in equation (3), we get b=1000200b=800
Now substituting c=1000 in equation (2), we get 1000=2a2002a=1200a=600
Hence the lengths of the sides are 600 ft, 800 ft and 1000 ft
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Jeffrey Jordon
Answered 2021-10-27 Author has 2064 answers

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