If the ratio of the lengths of two sides of a triangle is 7:9 and the longer sid

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Question: If the ratio of the lengths of two sides of a triangle is 7:9 and the longer side is 36 cm, what is the length of the shorter side?

Options:

Correct Answer: 28

Solution:

Let the shorter side be 7x and the longer side be 9x. Given 9x = 36, x = 4. Therefore, shorter side = 7x = 7*4 = 28.

If the ratio of the lengths of two sides of a triangle is 7:9 and the longer side is 36 cm, what is the length of the shorter side?

If the ratio of the lengths of two sides of a triangle is 7:9 and the longer side is 36 cm, what is the length of the shorter side?

Step 1: Understand the ratio of the sides. The ratio is 7:9, which means for every 7 parts of the shorter side, the longer side has 9 parts.
Step 2: Assign variables to the sides based on the ratio. Let the shorter side be 7x and the longer side be 9x.
Step 3: We know the longer side is 36 cm. So, we can write the equation: 9x = 36.
Step 4: Solve for x by dividing both sides of the equation by 9. This gives us x = 36 / 9, which simplifies to x = 4.
Step 5: Now, find the length of the shorter side by substituting x back into the expression for the shorter side: 7x = 7 * 4.
Step 6: Calculate 7 * 4, which equals 28. Therefore, the length of the shorter side is 28 cm.

Ratio and Proportion – Understanding how to set up and solve problems involving ratios, particularly in the context of geometric figures like triangles.
Algebraic Manipulation – Applying algebra to solve for unknowns in equations derived from the given ratios.