If the ratio of the lengths of two sides of a triangle is 3:4 and the perimeter

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Question: If the ratio of the lengths of two sides of a triangle is 3:4 and the perimeter is 70 cm, what is the length of the shorter side?

Options:

Correct Answer: 21

Solution:

Let the sides be 3x and 4x. Then, 3x + 4x = 70, 7x = 70, x = 10. Therefore, the shorter side = 3x = 3*10 = 30.

If the ratio of the lengths of two sides of a triangle is 3:4 and the perimeter is 70 cm, what is the length of the shorter side?

If the ratio of the lengths of two sides of a triangle is 3:4 and the perimeter is 70 cm, what is the length of the shorter side?

Step 1: Understand that the ratio of the lengths of the two sides of the triangle is 3:4.
Step 2: Let the shorter side be represented as 3x and the longer side as 4x, where x is a common multiplier.
Step 3: Write the equation for the perimeter of the triangle. The perimeter is the sum of all sides, which is 3x + 4x.
Step 4: Combine the terms in the equation: 3x + 4x = 7x.
Step 5: Set the equation equal to the given perimeter: 7x = 70.
Step 6: Solve for x by dividing both sides of the equation by 7: x = 70 / 7 = 10.
Step 7: Now, find the length of the shorter side by substituting x back into the expression for the shorter side: 3x = 3 * 10.
Step 8: Calculate the length of the shorter side: 3 * 10 = 30 cm.

Ratio and Proportion – Understanding how to express relationships between quantities using ratios and how to use them to find unknown values.
Perimeter of a Triangle – Applying the concept of perimeter to relate the lengths of the sides of a triangle.
Algebraic Manipulation – Solving equations to find the value of a variable based on given conditions.