Question

Areas of two similar triangles are 225 sq. CM. If a side of the smaller triangle is 12 CM ,then find corresponding side of the bigger triangle.​

Answer 1

Solution :

the ratio of area of 2 similar triangle is equal to ratio of the square of the corresponding sides

Now,

let x be the Requird side and the bigger triangle

Area of bigger triangle/Area of smaller triangle = x²/12²

225/81 = x²/144

x² = 225 x 144/81

x² = (15 x 12)²/9²

x = 15 x 12/9

x = 4/5

x = 20cm

=> 20cm is the corresponding side of the bigger triangle.

Answer 2

Answer:

The question is wrong, it is 225cm² and 81cm²

Let's draw the triangles (I am using a Microsoft paint for the triangles)

In the figure, let PQ=12cm be the side of the smaller triangle.

We need to find out the corresponding side of the bigger triangle, that is, AB.

Now, we know that:

$\frac{ar(ABC)}{ar(PQR)}=\frac{AB^{2} }{PQ^{2} }$

$\frac{225}{81}=\frac{AB^{2} }{12^{2} }$

$AB=\sqrt{\frac{225*12^{2} }{81} }$

$AB=\frac{15*12}{9}$

$AB=20cm.$

The corresponding side of the bigger triangle is 20cm.

HOPE THIS HELPS :D