Question

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

Answer 1

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:

$a + 2a + 13 + a = 169\\4a+13=169\\4a=169-13\\4a=156\\a=\frac{156}{4}\\a=39$

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