One side of a triangle is half the longest side. The third side is 7 less than the longest side. The perimeter is 53 feet. Find the three sides

Let x = longest side of the triangle

x + x/2 + (x-7) = 53

Solve for x, then x/2 and x-7.

Let's represent the longest side of the triangle as "x".

According to the problem, one side of the triangle is half the longest side, so the second side can be represented as "x/2".

The third side is 7 less than the longest side, so it can be represented as "x - 7".

The perimeter of a triangle is the sum of all its sides. Therefore, we have the equation:

x + x/2 + (x - 7) = 53

To solve this equation, we need to combine like terms:

(2x + x + 2(x - 7))/2 = 53

Simplifying further:

(2x + x + 2x - 14)/2 = 53

Combining like terms again:

5x - 14 = 106

To isolate "x", we can add 14 to both sides of the equation:

5x = 120

Then, we divide both sides by 5:

x = 24

Now that we know the value of "x", we can find the lengths of the three sides:

Longest side: x = 24 feet
Second side: x/2 = 24/2 = 12 feet
Third side: x - 7 = 24 - 7 = 17 feet

Therefore, the lengths of the three sides of the triangle are 24 feet, 12 feet, and 17 feet.

To solve this problem, we need to set up equations using the given information and then solve for the unknown sides.

Let's start by representing the longest side as "x".

According to the problem, one side of the triangle is half the longest side. Therefore, the length of this side would be 0.5x.

The third side is 7 less than the longest side, so its length would be x - 7.

The perimeter of a triangle is the sum of the lengths of all three sides. We're given that the perimeter is 53 feet. Therefore, we can set up the equation:

x + 0.5x + (x - 7) = 53

Now, let's solve this equation to find the value of x, which represents the longest side.

Combining like terms:
2.5x - 7 = 53

Adding 7 to both sides:
2.5x = 60

Dividing both sides by 2.5:
x = 24

Now that we have the value of x, we can find the lengths of the other two sides:

One side is half the longest side:
0.5x = 0.5 * 24 = 12

The third side is 7 less than the longest side:
x - 7 = 24 - 7 = 17

Therefore, the three sides of the triangle are 17 feet, 12 feet, and 24 feet, respectively.