Question

# For a scale factor greater than 1, the ratio of the area of triangle to be constructed to the area of the given triangle will always be

A
Less than 1
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B
Greater than 1
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C
Equal to 1
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D
Equal to 2
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Solution

## The correct option is B Greater than 1Let the scale factor be m : n. Then, mn>1. ⇒m>n Let the triangle to be constructed be ΔABC and the given triangle be ΔPQR. As ΔABC∼ΔPQR ⇒ΔABC is a triangle whose sides are mn of the corresponding sides of ΔPQR Thus,ABPQ=BCQR=CARP=mn.......(ii) (Ratio of corresponding sides of similar tringales are equal) Now,Area(ΔABC)Area(ΔPQR)=(ABPQ)2(Ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.) ⇒Area(ΔABC)Area(ΔPQR)=(mn)2.......(iii) [Using (ii)] Also, m>n [From (i)] Squaring both sides, we get m2>n2 ⇒mn>1 ⇒(mn>1) ⇒Area(ΔABC)Area(ΔPQR)>1 [From (iii)] Thus, the ratio of the area of triangle to be constructed (ΔABC) to the area of triangle given (ΔPQR) is greater than 1. Hence, the correct answer is option d.

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