the perimeter of a triangle is 53 inches.the second side is 3 inches longer that the first side the third side is 1.5 times the lenght of the second side. what is the lenght of each side
x + (x + 3) + 1.5(x + 3) = 53
Solve for x.
To find the lengths of the sides of the triangle, we can use the given information and set up equations to solve for each length.
Let's assign variables to represent the lengths of the sides. Let's call the length of the first side "x" inches. So the second side would be "x + 3" inches, and the third side would be "1.5 * (x + 3)" inches.
According to the given information, the perimeter of the triangle is 53 inches. The perimeter of a triangle is the sum of the lengths of its sides. So we can write the equation:
x + (x + 3) + 1.5 * (x + 3) = 53
Now we can solve this equation to find the value of "x" and then determine the lengths of the sides.
Expanding the equation:
x + x + 3 + 1.5x + 4.5 = 53
Combining like terms:
3.5x + 7.5 = 53
Subtracting 7.5 from both sides:
3.5x = 45.5
Dividing both sides by 3.5:
x = 13
So the length of the first side is 13 inches.
Using this value, we can find the lengths of the other sides:
Second side: x + 3 = 13 + 3 = 16 inches
Third side: 1.5 * (x + 3) = 1.5 * (13 + 3) = 1.5 * 16 = 24 inches
Therefore, the lengths of the sides of the triangle are:
First side: 13 inches
Second side: 16 inches
Third side: 24 inches