The lengths of the sides of a triangle are in ratio 2:4:5. The perimeter of the triangle is 44 cm. Find the lengths of the sides.
To find the lengths of the sides of the triangle, we can set up a proportion using the given ratio and the perimeter.
Let's represent the lengths of the sides as 2x, 4x, and 5x, where x is a common factor.
The perimeter of a triangle is the sum of its side lengths, so we can write the equation:
2x + 4x + 5x = 44
Simplifying the equation:
11x = 44
Dividing both sides of the equation by 11:
x = 4
Now we can find the lengths of the sides by substituting x back into our expression: 2x, 4x, and 5x.
The lengths of the sides are:
- The first side: 2x = 2(4) = 8 cm
- The second side: 4x = 4(4) = 16 cm
- The third side: 5x = 5(4) = 20 cm
Therefore, the lengths of the sides of the triangle are 8 cm, 16 cm, and 20 cm.
To find the lengths of the sides of the triangle, we need to use the given information that the lengths are in a ratio of 2:4:5 and the perimeter is 44 cm.
Step 1: Write the ratio in terms of a common factor.
The given ratio is 2:4:5. We can simplify this ratio by dividing all the numbers by their greatest common factor (GCF), which in this case is 1. After simplifying, the ratio becomes 2:4:5.
Step 2: Assign variables to the lengths of the sides.
Let's assign variables to the lengths of the sides, such as 2x, 4x, and 5x. This way, we can express the sides of the triangle in terms of the same variable x.
Step 3: Set up an equation for the perimeter of the triangle.
The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is given as 44 cm, so we can set up an equation:
2x + 4x + 5x = 44
Step 4: Solve the equation for x.
Combine like terms: 2x + 4x + 5x = 44, which simplifies to 11x = 44.
Divide both sides by 11 to solve for x: x = 4.
Step 5: Find the lengths of the sides.
Now that we have the value of x, we can substitute it back into our expressions for the side lengths:
- First side: 2x = 2(4) = 8 cm
- Second side: 4x = 4(4) = 16 cm
- Third side: 5x = 5(4) = 20 cm
Therefore, the lengths of the sides of the triangle are 8 cm, 16 cm, and 20 cm.
2 x + 4 x + 5 x = 44
11 x = 44
x = 4
2 x = 8 etc