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.
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.
Show Hint
In similar triangles, use the ratio of perimeters to find the ratio of corresponding sides.
Updated On: Jul 13, 2025
Hide Solution
Verified By Collegedunia
Solution and Explanation
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
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
Was this answer helpful?
0
1
Top Questions on Triangles
- In the given figure, AB \(||\) DE and BD \(||\) EF. Prove that \(DC^2 = CF \times AC\).
- Assertion (A) : \(\triangle ABC \sim \triangle PQR\) such that \(\angle A = 65^\circ\), \(\angle C = 60^\circ\). Hence \(\angle Q = 55^\circ\).
Reason (R) : Sum of all angles of a triangle is \(180^\circ\). - If the orthocentre of the triangle formed by the lines $ y = x + 1 $, $ y = 4x - 8 $, and $ y = mx + c $ is at $ (3, -1) $, then $ m - c $ is:
In the adjoining figure, \( AP = 1 \, \text{cm}, \ BP = 2 \, \text{cm}, \ AQ = 1.5 \, \text{cm}, \ AC = 4.5 \, \text{cm} \) Prove that \( \triangle APQ \sim \triangle ABC \).
Hence, find the length of \( PQ \), if \( BC = 3.6 \, \text{cm} \).
- ABC is an isosceles right triangle with C as right angle. Prove that \(AB^2 = 2AC^2\).
View More Questions
Questions Asked in CBSE X exam
- If \(\sqrt{3} \sin \theta = \cos \theta\), then value of \(\theta\) is
- CBSE Class X - 2025
- Trigonometry
- The journeys of Anne Frank and Valli teach us the vital lesson that optimism and self-assurance empower women to rise above circumstances and overcome obstacles. Examine the similarities.
- CBSE Class X - 2025
- From the Diary of Anne Frank
- Suggest any two ways to increase women's representation in leadership roles.
- CBSE Class X - 2025
- Gender, Religion and Caste
- You are Mahima/Manoj, a resident of B/20, Shastri Road, Mumbai, and a volunteer with ‘Clean India’. As a concerned citizen, you have noticed that Marine Lines has become heavily polluted with plastic and garbage.
Write a letter to the editor of a prominent newspaper to raise awareness about this issue. In your letter, explain how environmental damage can be reduced through the help of NGOs, individuals, and government organizations.- CBSE Class X - 2025
- Letter Writing
- Out of the two media - Medium 1 and Medium 2, in which is the speed of light more?
- CBSE Class X - 2025
- Light - Reflection and Refraction
View More Questions