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Mathematics [1 Mark Question Answer]

Similarity · ICSE STD 10 (ICSE - English Medium). 3 questions.

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[1 Mark Question Answer]

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Question 11 Mark
Triangles ABC and DEF are similar.
If AC = 19 cm and DF = 8 cm, find the ratio between the areas of two triangles.
Answer
In ΔABC and ΔDEF, AC = 19 cm, DF = 8 cm.
Since, $\frac{\operatorname{area}(\triangle ABC )}{\operatorname{area}(\triangle DEF )}=\frac{ AC ^2}{ DF ^2}=\frac{(19)^2}{(8)^2}=\frac{361}{64}$
Hence, the required ratio is 361: 64.
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Question 21 Mark
In the adjoining figure, $\triangle ACB \sim \triangle APQ.$ If $BC = 10 cm, PQ = 5 cm, BA = 6.5 cm$ and $AP = 2.8 cm$ find the area $(\triangle ACB):$ area $(\triangle APQ).$
Answer
$\triangle ACB \sim \triangle APQ.$
Then, $\frac{\operatorname{area}(\triangle ACB )}{\operatorname{area}(\triangle APQ )}=\frac{ BC ^2}{ PQ ^2}$
$=\frac{(10)^2}{(5)^2}$
$=\frac{100}{25}$
$=\frac{4}{1}$
Required ratio is $4 : 1.$
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Question 31 Mark
Triangles ABC and DEF are similar.
If AC = 19 cm and DF = 8 cm, find the ratio between the area of two triangles.
Answer
In ΔABC and ΔDEF, AC = 19 cm, DF = 8 cm.
Since, $\frac{\operatorname{area}(\Delta ABC )}{\operatorname{area}(\Delta DEF )}=\frac{ AC ^2}{ DF ^2}=\frac{(19)^2}{(8)^2}=\frac{361}{64}$
Hence, the required ratio is 361: 64.
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[1 Mark Question Answer] - Mathematics STD 10 Questions - Vidyadip