If the lengths of the sides of a triangle are in the ratio 3:4:5 and the perimet

₹0.0

Question: If the lengths of the sides of a triangle are in the ratio 3:4:5 and the perimeter is 60 cm, what is the length of the longest side?

Options:

Correct Answer: 20 cm

Solution:

Let the sides be 3x, 4x, 5x. Then, 3x + 4x + 5x = 60. Therefore, 12x = 60, x = 5. Longest side = 5x = 25 cm.

If the lengths of the sides of a triangle are in the ratio 3:4:5 and the perimeter is 60 cm, what is the length of the longest side?

If the lengths of the sides of a triangle are in the ratio 3:4:5 and the perimeter is 60 cm, what is the length of the longest side?

Step 1: Understand that the sides of the triangle are in the ratio 3:4:5.
Step 2: Let the sides of the triangle be represented as 3x, 4x, and 5x, where x is a common multiplier.
Step 3: Calculate the perimeter of the triangle by adding the lengths of the sides: 3x + 4x + 5x.
Step 4: Simplify the equation: 3x + 4x + 5x = 12x.
Step 5: Set the equation equal to the given perimeter: 12x = 60.
Step 6: Solve for x by dividing both sides of the equation by 12: x = 60 / 12.
Step 7: Calculate x: x = 5.
Step 8: Find the length of the longest side, which is 5x: 5 * 5 = 25 cm.

Ratios – Understanding and applying ratios to determine the lengths of triangle sides.
Perimeter – Calculating the perimeter of a triangle and using it to find unknown side lengths.
Triangle Properties – Recognizing that a triangle with sides in the ratio 3:4:5 is a right triangle.