he sides of a triangle are in the ratio 3 4  and its perimeter is 72 find all sides of triangle

The sides of the triangle are given in the ratio 3:4, and the perimeter is 72 units. To find the lengths of all sides of the triangle, let's set up the solution.

### Step 1: Express the sides in terms of a variable
Let the sides of the triangle be \( 3x \) and \( 4x \), where \( x \) is a constant multiplier for the ratio.

Since the triangle has three sides, and we know two of them are \( 3x \) and \( 4x \), the third side will also follow from the perimeter. In a right triangle, we usually deal with ratios like \( 3:4:5 \) for the sides. So, the third side would be \( 5x \).

### Step 2: Write the equation for the perimeter
The perimeter of the triangle is the sum of all three sides, which gives:
\[
3x + 4x + 5x = 72
\]
\[
12x = 72
\]

### Step 3: Solve for \( x \)
\[
x = \frac{72}{12} = 6
\]

### Step 4: Find the lengths of all sides
Now that we have \( x = 6 \), we can find the lengths of the sides:
- First side: \( 3x = 3 \times 6 = 18 \)
- Second side: \( 4x = 4 \times 6 = 24 \)
- Third side: \( 5x = 5 \times 6 = 30 \)

### Final Answer:
The sides of the triangle are **18 units**, **24 units**, and **30 units**.

Would you like more details or explanations?

Here are 5 related questions for practice:
1. If the perimeter were 90 units, what would the sides of the triangle be?
2. What is the area of the triangle with sides 18, 24, and 30 units?
3. Can a triangle with side lengths in the ratio 3:4:5 be an isosceles triangle?
4. What is the length of the hypotenuse of a right triangle whose other two sides are 9 units and 12 units?
5. If the perimeter of a triangle is 120 units and the ratio of its sides is 5:12:13, what are the lengths of the sides?

**Tip:** When dealing with ratios of triangle sides, try to spot patterns like the common 3:4:5 ratio for right triangles, which simplifies the problem-solving process.

The sides of a triangle are in the ratio 3:4, and its perimeter is 72. Find all sides of the triangle.

Learn how to determine the side lengths of a triangle with a perimeter of 72 units, given that the sides are in the ratio 3:4. This solution explores key mathematical concepts such as ratios, perimeter, and the Pythagorean theorem, suitable for students in Grades 6-8.

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