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.

Algebra ->  Test -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
let c be the longest side, a second and b third side
given:
first use this: the third side is 12ft less then the longest side

b%2B12ft=c...........1

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

a=c%2F2............2

The perimeter is P=53ft, means a%2Bb%2Bc=53ft........3
________________________________

b%2B12ft=c...........1

a=c%2F2............2

a%2Bb%2Bc=53ft........3
________________________________solve this system

a%2Bb%2Bc=53ft........3...plug in a=c%2F2 from 2

c%2F2%2Bb%2Bc=53ft......3a..go to 1 and solve for b


b%2B12ft=c...........1

b=c-12ft...........plug it in 3a


c%2F2%2B%28c-12ft%29%2Bc=53ft....solve for c

c%2F2%2Bc-12ft%2Bc=53ft

c%2F2%2B2c=53ft%2B12ft

c%2F2%2B2c=65ft........both sides multiply by 2

2c%2F2%2B2%2A2c=2%2A65ft

c%2B4c=130ft

5c=130ft

c=130ft%2F5

highlight%28c=26ft%29

go to b=c-12ft and find b

b=26ft-12ft

highlight%28b=14ft%29

and finally, go to a=c%2F2....2 and find a

a=26ft%2F2

highlight%28a=13ft%29














Answer by DrBeeee(684) About Me  (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.