Question

If the areas of two similar triangles are 81 cm\(^2\) and 49 cm\(^2\) respectively. If the altitude of the smaller triangle is 3.5 cm, then the corresponding altitude of the bigger triangle is:

• A. 9.5 cm
• B. 9 cm
• C. 7 cm
• D. 4.5 cm

Hint:

For similar triangles, the ratio of their areas is the square of the ratio of their corresponding sides or altitudes.

Answer 1

The Correct Option is A

The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides, including the corresponding altitudes. Let the corresponding altitude of the bigger triangle be \(x\). The ratio of the areas is: \[ \frac{81}{49} = \left(\frac{x}{3.5}\right)^2 \] Taking square roots on both sides: \[ \frac{9}{7} = \frac{x}{3.5} \] Solving for \(x\): \[ x = \frac{9}{7} \times 3.5 = 9.5 \, \text{cm} \] Thus, the correct answer is option (1).