The ratio of the side lengths of a triangle. Is 2:4:5 and the perimeter is 55 cm. What is the length of the shortest side?
let the sides be 2x, 4x, and 5x
solve for x
2x + 4x + 5x = 55
sub your x value into 2x
To find the length of the shortest side of the triangle, we need to determine the value of the smallest ratio.
The given ratio is 2:4:5. We can calculate the actual lengths of the sides by multiplying each ratio value by a constant. Let's assume this constant is x.
So, the side lengths would be 2x, 4x, and 5x.
Since the perimeter of the triangle is 55 cm, we can write the equation:
2x + 4x + 5x = 55
Combine like terms:
11x = 55
To solve for x, divide both sides of the equation by 11:
x = 55/11
x = 5
Now, we can substitute the value of x back into the side lengths:
Shortest side = 2x = 2 * 5 = 10 cm
Therefore, the length of the shortest side of the triangle is 10 cm.
To find the length of the shortest side, we need to determine the actual lengths of the triangle's sides. Given that the ratio of the side lengths is 2:4:5, we can let the common ratio be represented by "x."
Let's assign the lengths of the sides as 2x, 4x, and 5x. Since the perimeter of a triangle is the sum of all its sides, we can set up an equation as follows:
2x + 4x + 5x = 55
Combining like terms, we get:
11x = 55
To find the value of x, we divide both sides of the equation by 11:
x = 55 / 11
x = 5
Now that we know x is 5, we can find the length of the shortest side by substituting x back into the equation. The shortest side is represented as 2x, so:
Shortest side = 2 * x
Shortest side = 2 * 5
Shortest side = 10 cm
Therefore, the length of the shortest side of the triangle is 10 cm.