Flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 13 feet more than the length of the shortest side. find the dimensions if the perimeter is 169 feet

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:

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

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