Question

Areas of two similar triangles are 25 and 16. The ratio of the perimeters of the triangles is ........,Fill in the blank so that the given statement is true.

Answer 1

Hi ,

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If two triangles are similar ,

ratio of their perimeters equal to

ratio of their corresponding square

roots of areas.

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Let A1 and A2 are areas of two triangles,

P1 and P2 are their corresponding

perimeters.

It is given that ,

A1 = 25 , A2 = 16

P1/P2 = √( A1)/A2

= √ (25/16 )

= 5/4

P1 : P2 = 5 : 4

Answer : 5 : 4

I hope this helps you.

: )

Answer 2

we know two important concepts
1. Ratio of areas of two similar triangles = Ratio of the squares of the corresponding sides.

2. Ratio of perimeter of two similar triangles = Ratio of corresponding sides.

so, from (1) and (2), we can say that
ratio of two similar triangles = ratio of the square of perimeter of two similar triangles.

e.g., $\bf{\frac{\Delta_1}{\Delta_2}=\frac{perimeter_1^2}{perimeter_2^2}}$
so, 25/16 = (ratio of perimeter)²
=> ratio of perimeter = 5/4

hence, answer is 5 : 4