A triangle A-BC- is constructed similar to - ABC with a scale factor 34- then the ratio of areas of - A-BC- and - ABC will be

Given:Δ P'QR'∼Δ PQR ∴Area (Δ P'QR')Area (Δ PQR)= (Ratio of corresponding sides)^2 =(34)^2(∵ Scale factor =34) =916 ⇒ Area (Δ P'QR):Area (Δ ABC)=9:16 Hence, th ...

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Standard VII

Mathematics

Area of Triangle Between Two Parallels

A triangle A′...

Question

A triangle A′BC′ is constructed similar to $Δ A B C$ with a scale factor $\frac{3}{4}$ , then the ratio of areas of $Δ A' B C' a n d Δ A B C$ will be

3:2

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9:16

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6:5

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3:1

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Solution

The correct option is B 9:16
Given: $Δ P^{'} Q R^{'} \sim Δ P Q R$
$∴ \frac{A r e a (Δ P^{'} Q R^{'})}{A r e a (Δ P Q R)} = (Ratio of corresponding sides)^{2}$
$= {(\frac{3}{4})}^{2} (∵ S c a l e f a c t o r = \frac{3}{4})$
$= \frac{9}{16}$

$\Rightarrow A r e a (Δ P^{'} Q R) : A r e a (Δ A B C) = 9 : 16$

Hence, the correct answer is option b.

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A triangle A′BC′ is constructed similar to ΔABC with a scale factor 34, then the ratio of areas of ΔA'BC'and ΔABC will be

The correct option is B 9:16Given:ΔP′QR′∼ΔPQR ∴Area(ΔP′QR′)Area(ΔPQR)=(Ratio of corresponding sides)2 =(34)2(∵Scalefactor=34) =916 ⇒Area(ΔP′QR):Area(ΔABC)=9:16 Hence, the correct answer is option b.

A triangle A′BC′ is constructed similar to $Δ A B C$ with a scale factor $\frac{3}{4}$ , then the ratio of areas of $Δ A' B C' a n d Δ A B C$ will be