One side of a triangle is half the longest side. The third side is 10 meters less than the longest side. The perimeter is 45 meters. Find all three sides
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To find the sides of the triangle, we can use the given information and set up some equations.
Let's denote the longest side as "x".
According to the problem, one side of the triangle is half the longest side. So, the other side can be represented as "0.5x".
The third side is given as 10 meters less than the longest side. Therefore, it can be represented as "x - 10".
The perimeter of a triangle is the sum of its three sides. So, we can write the equation:
x + 0.5x + (x - 10) = 45
Now, let's solve this equation to find the value of "x".
Combining the like terms, we have:
2x - 10 = 45
Adding 10 to both sides of the equation:
2x - 10 + 10 = 45 + 10
2x = 55
Dividing both sides of the equation by 2:
(2x)/2 = 55/2
x = 27.5
So, the longest side of the triangle is 27.5 meters.
To find the other two sides, we substitute the value of x into our expressions:
One side = 0.5x = 0.5 * 27.5 = 13.75 meters
Third side = x - 10 = 27.5 - 10 = 17.5 meters
Therefore, the three sides of the triangle are 13.75 meters, 27.5 meters, and 17.5 meters.