SOLUTION: One side of a triangle is half the longest side.the third side is 12 ft less then the longest side. The perimeter is 53 ft. Find all three sides.

Question 658963: One side of a triangle is half the longest side.the third side is 12 ft less then the longest side. The perimeter is 53 ft. Find all three sides.
Found 2 solutions by MathLover1, DrBeeee:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
let be the longest side, second and third side
given:
first use this: the third side is less then the longest side

...........1

then, one side of a triangle is half the longest side:

............2

The perimeter is , means ........3
________________________________

...........1

............2

........3
________________________________solve this system

........3...plug in from 2

......3a..go to 1 and solve for

...........1

...........plug it in 3a

....solve for

........both sides multiply by

go to and find

and finally, go to ....2 and find

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let c = the longest side
Let a = one side
Let b = the other side
The perimeter, p, is given by
(1) p = a + b + c
From the problem statement we have
(2) a = c/2 and
(3) b = c - 12
Substitute (2) and (3) into (1) and get
(4) p = c/2 + c - 12 + c or
(5) p = (5/2)c - 12
Using the given value of p yields
(6) (5/2)c - 12 = 53 or
(7) (5/2)c = 65 or
(8) 5c = 130 or
(9) c = 26
Then
a = 13 and b = 14.
Let's check these values.
Is (26+13+14 = 53)?
Is (53 = 53)? Yes
Answer: The three sides of the triangle are 26, 13 and 14 units in lenght.

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