A triangle has a perimeter of 112 centimeters, each of the two longer sides of the triangle is three times as long as the shortest side. Find the length of each side of the triangle
short side = x
both long sides = 3x
x + 3x + 3x = 112
x + 6x = 112
7x = 112
divide both sides by 7
x = 16; 3x = 48
Let's denote the length of the shortest side as x.
According to the information given, each of the two longer sides is three times as long as the shortest side.
So, the lengths of the two longer sides would be 3x.
The perimeter of the triangle is given as 112 centimeters, which means that the sum of all three sides is 112.
Therefore, we can write the equation: x + 3x + 3x = 112.
Combining like terms, we get: 7x = 112.
To isolate x, we divide both sides of the equation by 7: x = 112/7.
Simplifying, we find that x = 16.
So, the length of the shortest side is 16 centimeters.
The lengths of the other two sides can be found by multiplying the length of the shortest side by 3: 3 * 16 = 48.
Therefore, the lengths of the two longer sides are 48 centimeters each.
To find the lengths of the sides of the triangle, let's set up some equations.
Let x represent the length of the shortest side.
Since each of the longer sides is three times as long as the shortest side, the lengths of the longer sides can be expressed as 3x and 3x.
The perimeter of a triangle is the sum of the lengths of its sides, so we can write the equation:
x + 3x + 3x = 112
Now, let's solve for x.
Combine like terms:
7x = 112
Divide both sides by 7 to isolate x:
x = 112 / 7
Simplify:
x = 16
The shortest side of the triangle has a length of 16 centimeters.
To find the lengths of the longer sides, we can substitute x = 16 into the previous equations:
Shorter side: x = 16 cm
Longer sides: 3x = 3 * 16 = 48 cm
Therefore, the lengths of the sides of the triangle are:
Shortest side: 16 cm
Longer sides: 48 cm, 48 cm
short side ---- x
each of other sides (must be isosceles) ---- 3x
x + 3x + 3x = 112
I will let you finish it