the perimeter of a triangle is 19 cm. if the length of the longest side is twice that of the shortest side and 3cm less than the sum of the lengths of the other two sides, find the length of the three sides
shortest side ---- x
longest side ----- 2x
middle side ---- y
longest side is also x+y-3
2x = x+y-3
x = y-3
y = x+3
sum = x+2x + y = 19
x+2x+(x+3) = 16
4x=16
x = 4
shortest side = 4
longest side = 8
middle side = 7
check:
they clearly add up to 19
is the longest side equal to 3 less than the sum of the other two ?
is 8 = 4+7 - 3 ? YES
To solve this problem, we need to set up equations based on the given information.
Let's assume that the shortest side of the triangle has a length of "x" cm.
According to the problem, the longest side is twice the length of the shortest side. So, the longest side is 2x cm.
The other two sides (which are not the longest side) have lengths such that the sum of the lengths is 3 cm more than the longest side. Mathematically, this can be expressed as:
x + (x + 3) + (2x - 3) = 2x + 3
Now, we can solve this equation to find the value of x:
x + x + 3 + 2x - 3 = 2x + 3
4x = 2x + 3
4x - 2x = 3
2x = 3
x = 3/2
x = 1.5 cm
So, the shortest side of the triangle is 1.5 cm.
From this, we can determine the lengths of the other two sides:
- The longest side is twice the shortest side, so it is 2 * 1.5 = 3 cm.
- The third side is the sum of the other two sides minus 3, so it is (1.5 + 3) - 3 = 1.5 cm.
Therefore, the lengths of the sides of the triangle are 1.5 cm, 1.5 cm, and 3 cm.