If the ratio of the areas of two similar triangles is 25 : 144, the ratio of their corresponding sides is:

Options
a) 12 : 5
b) 5 : 12
c) 25 : 12
d) 5 : 144

Solution

As per question
Let the two triangles be $ \Delta ABC $ and $ \Delta PQR $
It is given that $ \Delta ABC $ ~ $ \Delta PQR $
$ \frac {Area of \Delta ABC}{Area of \Delta PQR} = \frac{25}{144}$
By the similarity criterion , if two triangles are similar than the ratio of their area will be square of the ratio of their corresponding sides ,
$ \frac {\text{Area of} \Delta ABC}{\text{Area of} \Delta PQR} = (\frac{AB}{PQ})^2 $
$ (\frac{AB}{PQ})^2 = \frac {25}{144}$
$ \frac{AB}{PQ} = \sqrt \frac{25}{144}$
$ \frac{AB}{PQ} = \frac{5}{12}$
ratio of two similar triangles = 5 : 12

Ans: 5 : 12