two sides of a triangle are equal. The third side is 3 less than the sum of the two equal sides. The perimeter is 31 inches. Find the length of each side
one side= 8.5
one side= 8.5
one side = 14
The two sides equal 8.5 inches. The third side equals 14 inches.
8.5+8.5=17
17-3=14
14+17=31
Let x = length of each of the two sides. Then third side = 2x-3
2x + 2x -3 = 31
4x - 3 = 31
4x = 34
x = 8.5
2x - 3 = 17 -3 = 14
To find the length of each side of the triangle, we can start by assigning variables to the unknown sides. Let's call the length of the equal sides "x", and the length of the third side "y".
According to the problem, the two equal sides are equal, so we have x = x.
The third side is 3 less than the sum of the two equal sides. This can be expressed as:
y = x + x - 3
y = 2x - 3
The perimeter of a triangle is the sum of all its sides. In this case, the perimeter is given as 31 inches, so we can write the equation:
x + x + y = 31
Now we can substitute the expression for y into the equation and solve for x:
x + x + (2x - 3) = 31
4x - 3 = 31
4x = 34
x = 34/4
x = 8.5
Now we have the value of x, which gives us the length of the equal sides. To find the length of the third side, y, we substitute this value of x back into the expression we found earlier:
y = 2x - 3
y = 2(8.5) - 3
y = 17 - 3
y = 14
Therefore, the length of each equal side is 8.5 inches, and the length of the third side is 14 inches.