One side of triangle is 5 more than 2 times the shortest side. The third side is 23 feet more than the shortest side. The perimeter is 72. Find all three sides.
Let s = the shortest side.
s + 2s + 5 + s + 23 = 72
4s + 28 = 72
4s = 44
s = 11
Ah, we're doing some math here! Alright, let's solve this triangle puzzle together.
Let's call the shortest side "x". According to the problem, one side of the triangle is 5 more than 2 times the shortest side. So, the second side can be expressed as 2x + 5.
Now, the third side is 23 feet more than the shortest side. So, the length of the third side can be represented as x + 23.
To find the perimeter, we add up all three sides and set it equal to 72:
x + (2x + 5) + (x + 23) = 72.
Simplifying the equation, we have:
4x + 28 = 72.
Subtracting 28 from both sides:
4x = 44.
Dividing by 4:
x = 11.
Now that we know the shortest side is 11 feet, we can find the other sides:
Second side: 2x + 5 = 2(11) + 5 = 27 feet.
Third side: x + 23 = 11 + 23 = 34 feet.
Therefore, the three sides of the triangle are 11 feet, 27 feet, and 34 feet. Remember, the shortest side may not be the funniest, but it's an important part of the triangle!
Let's assume the shortest side of the triangle as x.
According to the given information, one side of the triangle is 5 more than 2 times the shortest side. Therefore, the second side can be expressed as (2x + 5).
The third side is 23 feet more than the shortest side. So, the third side can be expressed as (x + 23).
The perimeter of a triangle is the sum of the lengths of all three sides. In this case, the perimeter is 72. Therefore, we can set up the equation:
x + (2x + 5) + (x + 23) = 72
Now let's solve this equation step by step:
Combine like terms:
4x + 28 = 72
Subtract 28 from both sides:
4x = 44
Divide both sides by 4:
x = 11
Now we can substitute the value of x back into our equations to find the lengths of all three sides:
Shortest side = x = 11
Second side = 2x + 5 = 2(11) + 5 = 27
Third side = x + 23 = 11 + 23 = 34
Therefore, the lengths of all three sides of the triangle are 11, 27, and 34 feet, respectively.
Let's denote the shortest side of the triangle as x.
According to the problem, we know that one side of the triangle is 5 more than 2 times the shortest side, which can be expressed as: 2x + 5.
The third side is 23 feet more than the shortest side, so it can be expressed as x + 23.
The perimeter of a triangle is calculated by summing the lengths of all three sides. In this case, the perimeter is given as 72.
So we can set up the equation: x + (2x + 5) + (x + 23) = 72.
Simplifying this equation, we get: 4x + 28 = 72.
Subtracting 28 from both sides, we have: 4x = 44.
Dividing both sides by 4, we find: x = 11.
Now that we have the value of x (the shortest side), we can substitute it back into the expressions we found earlier to find the values of the other sides:
The first side is 2x + 5 = 2(11) + 5 = 27.
The third side is x + 23 = 11 + 23 = 34.
Hence, the three sides of the triangle are 11, 27, and 34 feet.