Answer :
Answer:
The dimensions of the triangle are 39 feet, 52 feet, and 78 feet
Step-by-step explanation:
Let the 3 sides of the triangle be a, b, and c
With a < b < c
a = shortest
b = middle
c = third side
One side twice the length of shortest, we can write:
b = 2a
Third side is 13 more than shortest, so we can write:
c = 13 + a
Perimeter (sum of all sides, a+b+c) is 169, so we can write:
a + b + c = 169
We replace this equation with the first 2, to get:
a + b + c = 169
a + 2a + 13 + a = 169
Now, we solve for a:
[tex]a + 2a + 13 + a = 169\\4a+13=169\\4a=169-13\\4a=156\\a=\frac{156}{4}\\a=39[/tex]
Now, b:
b = 2a
b = 2(39) = 78
Now c:
c = 13 + a
c = 13 + 39
c = 52
The dimensions of the triangle are 39 feet, 52 feet, and 78 feet