If the ratio of the sides of a triangle is 3:4:5, what is the length of the long

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Question: If the ratio of the sides of a triangle is 3:4:5, what is the length of the longest side if the perimeter is 36 cm? (2021)

Options:

Correct Answer: 15 cm

Exam Year: 2021

Solution:

Let the sides be 3x, 4x, and 5x. Then, 3x + 4x + 5x = 36. Thus, 12x = 36, giving x = 3. The longest side is 5x = 15 cm.

If the ratio of the sides of a triangle is 3:4:5, what is the length of the longest side if the perimeter is 36 cm? (2021)

If the ratio of the sides of a triangle is 3:4:5, what is the length of the longest side if the perimeter is 36 cm? (2021)

Step 1: Understand that the sides of the triangle are in the ratio 3:4:5.
Step 2: Let the sides be represented as 3x, 4x, and 5x, where x is a common multiplier.
Step 3: Add the sides together: 3x + 4x + 5x.
Step 4: Simplify the addition: 3x + 4x + 5x = 12x.
Step 5: Set the total equal to the perimeter: 12x = 36 cm.
Step 6: Solve for x by dividing both sides by 12: x = 36 / 12 = 3.
Step 7: Find the length of the longest side, which is 5x: 5x = 5 * 3 = 15 cm.

Ratio and Proportion – Understanding how to apply ratios to find the lengths of sides in a triangle.
Perimeter Calculation – Using the perimeter of a triangle to set up an equation to solve for unknowns.
Algebraic Manipulation – Solving for a variable in an equation derived from the perimeter.