Question

The perimeters of two similar triangles ∆ABC and ∆PQR are 35cm and 45cm

respectively, then the ratio of the areas of the two triangles is______________​

Answer 1

Answer:35/45=7/9

Step-by-step explanation:

Because ratio of Perimeter of two similar triangles =Triangle ABC/Triangle PQR

Answer 2

Answer: The ratio of area of triangle $\dfrac{49}{81}$

Step-by-step explanation:    

The perimeters of two similar triangles ∆ABC is  35cm and ∆PQR is 45cm  

Now as we know If the ratio of the perimeter of two similar given triangles is equal to the ratio of the corresponding sides

i.e.

$\dfrac{\text {Perimeter of }\triangle_1}{\text {Perimeter of }\triangle_2}= \dfrac{\text {side of }\triangle_1}{\text {side of }\triangle_2}-----(i)$

Now  as we know the ratio of area of two the similar triangles is equal to  ratio of the corresponding sides

$\dfrac{\text {area of }\triangle_1}{\text {area of }\triangle_2}= (\dfrac{\text {side of }\triangle_1}{\text {side of }\triangle_2})^2-----(ii)$

from (i) and (ii)

$\dfrac{\text {area of }\triangle_1}{\text {area of }\triangle_2}= (\dfrac{\text {Perimeter of }\triangle_1}{\text {Perimeter of }\triangle_2})^2\\\\ \dfrac{\text {area of }\triangle ABC}{\text {area of }\triangle PQR}= (\dfrac{35}{45} )^2=(\dfrac{7}{9} )^2= \dfrac{49}{81}$

Hence, the ratio of area of triangle $\dfrac{49}{81}$