The perimeter of a triangle is 126 inches. The longest side is 7 inches longer than the shortest side. The shortest side is 2 inches less than remaining side. Find the length of the shortest side.
The shortest side is 39 inches.
Let the 3 sides be a, b, and c where a is the longest and c the shortest.
By the question,
c+7 = a
c+2 = b
From the above information, we can calculate that,
a-5=b
a=5+b ----- equation (i)
Similarly,
a+b+c=126
c=126-a-b
a-7=126-a-b [since c+7=a, by the question so c=a-7.]
a+a=126+7-b
2a=133-b
2(5+b)=133-b
10+2b=133-b
2b+b=133-10
3b=123
b=123/3
b=41
Applying the value of b=41 in c+2=b, as it is given in the question.
c=b-2
c=41-2
c=39.
So the length of the shortest side is 39 inches.
Well, well, well, let's play a game of triangle detective!
Let's call the shortest side "x". According to the information given, the longest side is 7 inches longer than the shortest side, which means it's "x + 7".
Now, we also know that the shortest side is 2 inches less than the remaining side, so the remaining side is "x + 2".
To find the perimeter of a triangle, you add up the lengths of all three sides. So we can set up an equation:
x + (x + 2) + (x + 7) = 126
Now we can solve this equation to find the length of the shortest side. But hey, if you're ready for some math humor, here's a little triangle joke for you:
Why was the math book sad?
Because it had too many problems!
Okay, now back to the problem-solving business. Let's solve that equation:
3x + 9 = 126
Subtract 9 from both sides:
3x = 117
Divide both sides by 3:
x = 39
So the length of the shortest side is 39 inches. Ta-da!
Let's assume that the shortest side of the triangle is x inches.
According to the problem, the longest side is 7 inches longer than the shortest side. Therefore, the longest side is x + 7 inches.
The remaining side is 2 inches more than the shortest side. So, the remaining side is x + 2 inches.
Thus, the perimeter of the triangle can be expressed as:
Perimeter = shortest side + longest side + remaining side
126 = x + (x + 7) + (x + 2)
Simplifying the equation, we get:
126 = 3x + 9
Subtracting 9 from both sides of the equation, we get:
117 = 3x
Dividing both sides of the equation by 3, we get:
x = 39
Therefore, the length of the shortest side of the triangle is 39 inches.
To solve this problem, we'll use algebra to represent the relationships between the sides of the triangle and then solve for the unknown side.
Let's assume that the shortest side of the triangle is denoted by 'x' inches.
According to the problem, the longest side is 7 inches longer than the shortest side, so its length would be (x + 7) inches.
The remaining side is 2 inches longer than the shortest side, so its length would be (x + 2) inches.
The perimeter of a triangle is the sum of the lengths of all three sides. In this case, the perimeter is given as 126 inches.
So, we can write the equation:
x + (x + 7) + (x + 2) = 126
Now, let's simplify and solve the equation:
3x + 9 = 126
Subtract 9 from both sides:
3x = 117
Divide both sides by 3:
x = 39
Therefore, the length of the shortest side of the triangle is 39 inches.