The length of the sides of a triangle are consecutive integers Half of the perimeter is 14 more than the length of the longest side Find the perimeter?

The sides are A, A+1, and A+2.

The perimeter is [ A + (A+1) + (A+2) ] = 3A + 3

Half of the perimeter = 1/2(3A+3) = (A+2) + 14

1/2(3A+3) = A + 16

3A + 3 = 2A + 32

3A = 2A + 29

A = 29

The sides are 29, 30, and 31.

The perimeter is 29+20+31 = 90

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Check:

The perimeter = 29+30+31 = 90.

1/2 (90) = 45 = 14 + 31 yay!