SOLUTION: One side of triangle is one-third the longest side. The third side is 7 feet less than the longest side. The perimeter is 70. Find all three sides.

Algebra ->  Linear-equations -> SOLUTION: One side of triangle is one-third the longest side. The third side is 7 feet less than the longest side. The perimeter is 70. Find all three sides.       Log On


   

Question 1094582: One side of triangle is one-third the longest side. The third side is 7 feet less than the longest side. The perimeter is 70. Find all three sides.

Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let a = the longest side, b & c are other sides
:
Write an equation for each statement
:
One side of triangle is one-third the longest side.
b = 1%2F3a
The third side is 7 feet less than the longest side.
c = a - 7
The perimeter is 70.
a + b + c = 70
replace b with 1%2F3a; replace c with (a-7)
a + 1%2F3%7D%7D%5Da+%2B+%28a-7%29+=+70%0D%0A2%7B%7B%7B1%2F3a = 70 + 7
21%2F3a = 77
Convert to an improper fraction
7%2F3a = 77
a = 77%2F%287%2F3%29
a = 77+%2A+3%2F7
Cancel the 7
a = 11 * 3
a = 33 ft is the longest side
:
I'll let you find b and c, see that they add up 70






Answer by greenestamps(13208) About Me  (Show Source):
You can put this solution on YOUR website!

The algebra you need to do is nearly always easier if you can set up the problem using only one variable instead of 3.

Since the given information says the shortest side is one-third the longest side, to avoid fractions I would let x be the length of the shortest side, making the length of the longest side 3x. Then from the given information we can determine that the length of the third side is 3x-7.

So the three side lengths are x, 3x, and 3x-7; and the perimeter is 70:
x+%2B+3x+%2B+3x-7+=+70
7x-7+=+70
7x+=+77
x+=+11

The shortest side is 11; that makes the longest side 3*11 = 33 and the longest side 33-7 = 26.