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Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, an

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Question: Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what is the area of the second triangle if its longest side is 10 cm?

Options:

  1. 40 cm²
  2. 20 cm²
  3. 30 cm²
  4. 50 cm²

Correct Answer: 20 cm²

Solution: 

The ratio of the sides is 10/5 = 2. Area ratio = (2)² = 4. Area of first triangle = 6 cm². Area of second triangle = 6 * 4 = 24 cm².

Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, an

Practice Questions

Q1
Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what is the area of the second triangle if its longest side is 10 cm?
  1. 40 cm²
  2. 20 cm²
  3. 30 cm²
  4. 50 cm²

Questions & Step-by-Step Solutions

Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what is the area of the second triangle if its longest side is 10 cm?
  • Step 1: Identify the sides of the first triangle, which are 3 cm, 4 cm, and 5 cm.
  • Step 2: Determine the longest side of the first triangle, which is 5 cm.
  • Step 3: Identify the longest side of the second triangle, which is given as 10 cm.
  • Step 4: Calculate the ratio of the longest sides of the two triangles: 10 cm (second triangle) / 5 cm (first triangle) = 2.
  • Step 5: Since the triangles are similar, the ratio of their areas is the square of the ratio of their sides. So, area ratio = (2)² = 4.
  • Step 6: Calculate the area of the first triangle using the formula for the area of a triangle. The area of the first triangle is 6 cm².
  • Step 7: Multiply the area of the first triangle by the area ratio to find the area of the second triangle: 6 cm² * 4 = 24 cm².
  • Similarity of Triangles – Understanding that similar triangles have proportional sides and areas.
  • Area Calculation – Calculating the area of triangles using the formula for area and understanding the relationship between side lengths and area in similar figures.
  • Ratio of Areas – Knowing that the ratio of the areas of similar triangles is the square of the ratio of their corresponding side lengths.
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