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The lengths of the sides of the triangle are 922 mi. , 1300 mi. , 850 mi.
We have triangle which has a perimeter of 3072 mi. such that the shortest side measures 72 mi less than the middle side, and the longest side measures 378 mi more than the middle side.
We have to find the lengths of the three sides.
What is the formula to calculate the perimeter of triangle with sides a, b and c ?
The perimeter of the triangle is as follows -
P = a + b + c
According to question, we have -
Perimeter of triangle = 3072 mi
Assume that the length of middle side be x.
Then -
shortest side = x - 72
longest side = x + 378
Using the formula for finding the perimeter of triangle, we get -
P = a + b + c
3072 = x + x - 72 + x + 378
3072 + 72 - 378 = 3x
3x = 2766
x = 922
Therefore, the middle side = 922 mi.
longest side = 922 + 378 = 1300 mi.
shortest side = 922 - 72 = 850 mi.
Hence, the lengths of the sides of the triangle are 922 mi. , 1300 mi. , 850 mi.
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