Question

The perimeters of two similar triangles are 22 cm and 33 cm respectively. If one side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle.

Hint:

In similar triangles, use the ratio of perimeters to find the ratio of corresponding sides.

Answer 1

Given:
Perimeters of two similar triangles = 22 cm and 33 cm
One side of first triangle = 9 cm
Find the corresponding side of the second triangle.

Step 1: Recall property of similar triangles
Sides of similar triangles are proportional to their perimeters.

Step 2: Write the ratio of corresponding sides
\[ \frac{\text{Side of first triangle}}{\text{Side of second triangle}} = \frac{\text{Perimeter of first triangle}}{\text{Perimeter of second triangle}} \] \[ \Rightarrow \frac{9}{x} = \frac{22}{33} = \frac{2}{3} \]

Step 3: Solve for \(x\)
\[ 9 \times 3 = 2 \times x \implies 27 = 2x \implies x = \frac{27}{2} = 13.5 \]

Final Answer:
Length of corresponding side in second triangle = 13.5 cm