The backyard of a house is in the shape of a triangle. The longest side is 4 ft shorter than twice the shortest side. The third side is 4 ft less than the longest side. If the perimeter of the yard is 162 ft, what are the lengths of the sides?

Well, well, well, looks like we have a triangle problem on our hands. Let's put our thinking caps on and see what we can do.

Let's call the length of the shortest side "x" (because why not?).

According to the information given, the longest side is 4 ft shorter than twice the shortest side. So, the longest side is (2x - 4).

And the third side is 4 ft less than the longest side. So, the third side is (2x - 4 - 4), which simplifies to (2x - 8).

Now, to find the perimeter, we add up all the sides and set it equal to 162 ft:

x + (2x - 4) + (2x - 8) = 162

Now we just gotta solve that equation:

5x - 12 = 162

5x = 174

x = 34.8

But hold on a second! How can a side of a triangle be 34.8 ft? That's not really realistic, is it? So, there might be something wrong with the information given.

But hey, at least we had some fun with math, right? Keep that laughter going! 😄🤡

Let's denote the length of the shortest side as x ft.

According to the given information, the longest side is 4 ft shorter than twice the shortest side. Hence, the longest side can be represented as 2x - 4 ft.

The third side is 4 ft less than the longest side. Therefore, the third side can be expressed as (2x - 4) - 4 ft, which simplifies to 2x - 8 ft.

The perimeter of the yard is the sum of all three sides. So we add the lengths of the sides together:
x + (2x - 4) + (2x - 8) = 162 ft

Now, let's solve this equation step-by-step to find the value of x.

x + 2x - 4 + 2x - 8 = 162
5x - 12 = 162
5x = 162 + 12
5x = 174
x = 174 / 5
x ≈ 34.8

Since the length of a side cannot be negative, we discard the negative solution.

Therefore, the length of the shortest side is approximately 34.8 ft.

To find the lengths of the other two sides, substitute the value of x back into the expressions we obtained earlier:
Longest side = 2x - 4 ≈ 2(34.8) - 4 ≈ 65.6 ft
Third side = 2x - 8 ≈ 2(34.8) - 8 ≈ 61.6 ft

Thus, the lengths of the sides are approximately:
Shortest side: 34.8 ft
Longest side: 65.6 ft
Third side: 61.6 ft

To solve this problem, let's assign variables to represent the lengths of the sides of the triangle.

Let's denote the shortest side as "x" ft.

According to the information given, the longest side is 4 ft shorter than twice the shortest side, which can be expressed as (2x - 4) ft.

The third side is 4 ft less than the longest side, which can be expressed as (2x - 4) ft - 4 ft, or (2x - 8) ft.

The perimeter of a triangle is the sum of all its sides. In this case, the perimeter is given as 162 ft. So we can write the equation as:

x + (2x - 4) + (2x - 8) = 162

Now, let's solve for x by combining like terms:

5x - 12 = 162

Adding 12 to both sides of the equation:

5x = 174

And then dividing both sides by 5:

x = 34.8

Since the length of any side cannot be negative or a decimal in this case, we can round it to the nearest whole number.

So, the shortest side of the triangle is approximately 35 ft.

Now, we can substitute this value back into the expressions we found earlier to find the lengths of the other sides:

Longest side: 2x - 4 = 2(35) - 4 = 70 - 4 = 66 ft

Third side: 2x - 8 = 2(35) - 8 = 70 - 8 = 62 ft

Therefore, the lengths of the sides of the triangle are approximately 35 ft, 66 ft, and 62 ft.

s = shortest side

the three sides are thus
s, 2s-4 and 2s-4-4

s + 2s-4 + 2s-8 = 162
5s = 174
s=34.8

34.8 + 65.6 + 61.6 = 162