Question

13. The perimeters of two similar triangles AABC and APQR are 35 cm and 45 cm
respectively, then the ratio of the areas of the two triangles is ...
​

Answer 1

Answer: 49/81

Step-by-step explanation:

The perimeter of ∆ABC = 35 cm

And,  

The perimeter of ∆PQR = 45 cm

Since, if two triangles are similar then the perimeters of the triangles are proportional to the measures of their corresponding sides.

∴ [Perimeter of (∆ABC)] / [Perimeter of (∆PQR)]

=  =  =

=

=

Also, if two triangles are similar then the ratio of the areas of the triangles is equal to the square of ratio of their corresponding sides.

∴ [Area of (∆ABC)] / [Area of (∆PQR)]

=   [{AB}/{PQ}]^2 = [{AC}/{PR}]^2 = [{BC}/{QR}]^2

= [{7}/{9}]^2

= {49}/{81}

Thus, the ratio of their area is 49/81.