Question

the area of two similar triangles are 25 cm* and 121 cm* respectively.what is the ratio of their corresponding sides​

Answer 1

$\huge\tt\red{SoLutiOn}$

SINCE THE AREA OF TWO SIMILAR TRIANGLE ARE IN THE RATIO OF THE SQUARE OF THE CORRESPONDING SIDES.

$\frac{Area(∆ABC)}{Area(∆PQR) } = \frac{{AB}^{2}}{{PQ}^{2}} \\ \\ \frac{25}{121} = \frac{{AB}^{2}}{PQ}^{2}} \\ \\ \sqrt{\frac{25}{121}} = \frac{AB}{PQ} \\ \\ \frac{5}{11} = \frac{AB}{PQ}$

THEREFORE THE RATIO OF THEIR CORRESPONDING SIDES IS 5 : 11 .

Answer 2

The ratio would be 5 : 11

Step-by-step explanation:

Since, if two triangles are similar then their corresponding sides are in same proportion.

Consider the corresponding sides are in the proportion of a,

i.e. if x be the base and y be the height of a triangle,

Then the base of second triangle= ax, its height = ay

∵ Area of triangle = 1/2 × base × height,

Thus, the ratio of their areas = $\frac{1/2\times ax\times ay}{1/2\times x\times y}$

= a²

According to the question,

a² = $\frac{25}{121}$

$a=\sqrt{\frac{25}{121}}$

$a=\frac{\sqrt{25}}{\sqrt{121}}$

$\implies a =\frac{5}{11}$

Hence, corresponding sides are in the proportion of  5 : 11

#Learn more :

If the ratio of two similar triangles is 64:121 , then the ratio of their corresponding side is

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