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

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

Solution

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