Question

The ratio of corresponding sides of similar triangles is 3 : 5, then find the ratio of their areas.
(a) 9 : 16
(b) 9 : 25
(c) 16 : 25
(d) None of these

Answer 1

Hint: In this given problem, we are given the ratio of the corresponding sides of two similar triangles. We are trying to find the ratio of the areas of those triangles. We know that the ratio of area of two similar triangles is equal to the ratio of squares of their sides. Thus, by simplifying we will get our needed value.

Complete step by step solution:
According to the question, we are given the ratio of corresponding sides of similar triangles is 3 : 5. We are trying to find the value of the ratio of the areas of those triangles.
We know the ratio of area of two similar triangles is equal to the ratio of square of their sides.
So, the ratio of the areas of the triangle would be,
$={{\left( ratio\,of\,the\,sides \right)}^{2}}$
Now, putting the values, we get, $={{\left( 3:5 \right)}^{2}}$
Simplifying the result, we are getting, $={{\left( 3 \right)}^{2}}:{{\left( 5 \right)}^{2}}$
We can get our solution as, $=9:25$

So, the correct answer is “Option (b)”.

Note: In this problem, we have dealt with the properties of similar angles. Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.