Q1. If two triangles are similar with a ratio of their sides as 2:3, what is the ratio of their areas?
Solution:
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2/3)^2 = 4/9.
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Q2. If triangle DEF is similar to triangle GHI, and the lengths of DE and GH are 4 cm and 8 cm respectively, what is the ratio of their areas?
Solution:
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (4/8)^2 = 1/4.
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Q3. In similar triangles, if the ratio of the lengths of two corresponding sides is 2:3, what is the ratio of their areas?
Solution:
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2/3)^2 = 4/9.
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Q4. In a triangle, if the lengths of two sides are 7 cm and 24 cm, what is the minimum possible length of the third side?
Solution:
By the triangle inequality theorem, the length of the third side must be greater than the difference of the other two sides. Therefore, the minimum length = 24 - 7 = 17 cm.
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Q5. In triangle DEF, if DE = 6 cm, DF = 8 cm, and angle E = 90 degrees, what is the length of EF?
Solution:
Using the Pythagorean theorem, EF = √(DE^2 + DF^2) = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 cm.
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Q6. In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, is triangle JKL a right triangle?
Solution:
By the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2, so triangle JKL is a right triangle.
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Q7. If triangle GHI is similar to triangle JKL and the length of GH is 5 cm and JK is 10 cm, what is the ratio of their corresponding sides?
Solution:
The ratio of corresponding sides of similar triangles is equal to the ratio of any two corresponding sides. Therefore, the ratio is 5:10, which simplifies to 1:2.
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Q8. If two angles of a triangle are 50 degrees and 70 degrees, what is the third angle?
