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Triangle ABC is similar to triangle DEF and their areas are respectively 64 cm2and 121 cm2. If EF = 15.4 cm, then BC =
- a)18cm
- b)11.2cm
- c)11cm
- d)13cm
Correct answer is option 'B'. Can you explain this answer?
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Solution:
Given,
Area of triangle ABC = 64 cm²
Area of triangle DEF = 121 cm²
EF = 15.4 cm
We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
i.e., Area of triangle ABC / Area of triangle DEF = (AB/DE)² = (BC/EF)² = (CA/DF)²
Therefore, (AB/DE)² = 64/121
=> AB/DE = 8/11
Similarly, (BC/EF)² = 64/121
=> BC/EF = 8/11
=> BC = (8/11) × EF = (8/11) × 15.4 cm = 11.2 cm
Hence, the correct option is (B) 11.2 cm.
Given,
Area of triangle ABC = 64 cm²
Area of triangle DEF = 121 cm²
EF = 15.4 cm
We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
i.e., Area of triangle ABC / Area of triangle DEF = (AB/DE)² = (BC/EF)² = (CA/DF)²
Therefore, (AB/DE)² = 64/121
=> AB/DE = 8/11
Similarly, (BC/EF)² = 64/121
=> BC/EF = 8/11
=> BC = (8/11) × EF = (8/11) × 15.4 cm = 11.2 cm
Hence, the correct option is (B) 11.2 cm.
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Triangle ABC is similar to triangle DEF and their areas are respectively 64 cm2and 121 cm2. If EF = 15.4 cm, then BC =a)18cmb)11.2cmc)11cmd)13cmCorrect answer is option 'B'. Can you explain this answer?
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