If the ratio of the lengths of two sides of a triangle is 3:5 and the perimeter

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Question: If the ratio of the lengths of two sides of a triangle is 3:5 and the perimeter is 64 cm, what is the length of the longer side?

Options:

Correct Answer: 25

Solution:

Let the sides be 3x and 5x. Then, 3x + 5x = 64, 8x = 64, x = 8. Therefore, the longer side = 5x = 5*8 = 40.

If the ratio of the lengths of two sides of a triangle is 3:5 and the perimeter is 64 cm, what is the length of the longer side?

If the ratio of the lengths of two sides of a triangle is 3:5 and the perimeter is 64 cm, what is the length of the longer side?

Step 1: Understand that the ratio of the lengths of the two sides of the triangle is 3:5. This means if one side is 3 parts, the other side is 5 parts.
Step 2: Let's represent the lengths of the sides using a variable. We can say the first side is 3x and the second side is 5x, where x is a number we will find.
Step 3: The perimeter of the triangle is the total length around it, which is the sum of all its sides. In this case, we only have two sides, so we add them together: 3x + 5x.
Step 4: Combine the terms: 3x + 5x = 8x. So, the equation for the perimeter is 8x.
Step 5: We know the perimeter is 64 cm, so we can set up the equation: 8x = 64.
Step 6: To find x, divide both sides of the equation by 8: x = 64 / 8.
Step 7: Calculate the value of x: x = 8.
Step 8: Now, we can find the lengths of the sides. The longer side is represented by 5x. So, we calculate 5 * x.
Step 9: Substitute the value of x into the equation for the longer side: 5 * 8 = 40.
Step 10: Therefore, the length of the longer side is 40 cm.

Ratios – Understanding and applying ratios to represent the relationship between the lengths of the sides of a triangle.
Perimeter – Using the concept of perimeter to set up an equation based on the sum of the sides of a triangle.
Algebraic Manipulation – Solving for a variable in an equation to find the lengths of the sides.