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Mathematics

Triangles ABC and PQR are similar to each other, then :

  1. Ar.(△ABC)Ar.(△PQR)=BC2PQ2\dfrac{\text{Ar.(△ABC)}}{\text{Ar.(△PQR)}} = \dfrac{BC^2}{PQ^2}

  2. AB2PQ2=AC2PR2\dfrac{AB^2}{PQ^2} = \dfrac{AC^2}{PR^2}

  3. Ar.(△BAC)Ar.(△QPR)AB2QP2\dfrac{\text{Ar.(△BAC)}}{\text{Ar.(△QPR)}} \ne \dfrac{AB^2}{QP^2}

  4. AC2PR2=BC2PQ2\dfrac{AC^2}{PR^2} = \dfrac{BC^2}{PQ^2}

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Answer

We know that,

The areas of two similar triangles are proportional to the squares on their corresponding sides.

Ar.(△ABC)Ar.(△PQR)=AB2PQ2\Rightarrow \dfrac{\text{Ar.(△ABC)}}{\text{Ar.(△PQR)}} = \dfrac{AB^2}{PQ^2} …….(1)

Ar.(△ABC)Ar.(△PQR)=AC2PR2\Rightarrow \dfrac{\text{Ar.(△ABC)}}{\text{Ar.(△PQR)}} = \dfrac{AC^2}{PR^2} ………(2)

From equation (1) and (2), we get :

AB2PQ2=AC2PR2\Rightarrow \dfrac{AB^2}{PQ^2} = \dfrac{AC^2}{PR^2}

Hence, Option 2 is the correct option.

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