the sides of a triangle are in the ratio 6:8:10. the perimeter is 120cm. find the length of the shortest side
6x + 8x + 10x = 120cm,
24x = 120,
X = 5.
6x = 6 * 5 = 30cm = Shortest side.
Well, if the sides of the triangle are in the ratio 6:8:10, we can assume that the actual lengths of the sides are 6x, 8x, and 10x, where x is a common multiplier.
Now, let's find the value of x. We know that the perimeter of the triangle is 120cm. So, we can set up an equation:
6x + 8x + 10x = 120
Combining like terms:
24x = 120
Dividing both sides by 24:
x = 5
So, the actual lengths of the sides are 6x = 6 * 5 = 30cm, 8x = 8 * 5 = 40cm, and 10x = 10 * 5 = 50cm.
Therefore, the length of the shortest side is 30cm. It may be short in length, but it's still an important side of the triangle!
To find the length of the shortest side of the triangle, we first need to calculate the actual lengths of the sides.
Let's assume that the common ratio between each side length is represented by 'x'. So, the lengths of the sides can be written as:
Shortest side: 6x
Intermediate side: 8x
Longest side: 10x
We are given that the perimeter of the triangle is 120cm. The perimeter of a triangle is the sum of its side lengths. So, we can set up the equation:
Perimeter = Shortest side + Intermediate side + Longest side
120 = 6x + 8x + 10x
Now, combine the like terms:
120 = 24x
Next, divide both sides of the equation by 24 to solve for 'x':
x = 120/24
x = 5
Now that we know 'x' is equal to 5, we can find the length of the shortest side by substituting 'x' back into the expression for the shortest side length:
Shortest side = 6x = 6 * 5 = 30 cm
Therefore, the length of the shortest side of the triangle is 30 cm.