Question

the
sides of two similar triangles are in the ratio of 3:,5. Areas of
these triangles are in the ratio ?
1.) 3:5

2)9 : 25

3)25:9

4) 4:5​

Answer 1

GivEn:

• Ratio of sides of two similar triangles is 3:5

To find:

• Ratio of areas of these triangles.

SoluTion:

$\bf \underline{\bigstar\;As\;we\;know\;that\;:}$

If two triangles are similar than the ratio of their sides is equal to square of their corresponding sides.

$:\implies\sf \dfrac{Side\;of\;one\; triangle}{Side\;of\; Another\; triangle} = \bigg( \dfrac{Area\;of\;one\; triangle}{Area\;of\;another\;triangle} \bigg)$

━━━━━━━━━━━━

Therefore,

We have, Ratio of sides of two similar triangles = 3:5

$:\implies\sf Ratio_{\;(Areas)} = \bigg( \dfrac{3}{5} \bigg)^2$

$:\implies\sf Ratio_{\;(Areas)} = \dfrac{9}{25}$

$:\implies{\underline{\boxed{\sf{\purple{Ratio_{\;(Areas)} = 9:25}}}}}\;\bigstar$

$\therefore$ Ratio of areas of these triangles is 9:25.

★ Hence, Option (2) is correct.

Answer 2

Given ,

The sides of two similar triangles are in the ratio of 3 : 5

As we know that ,

The ratio of area of two similar Δ is equal to the square of ratio of their corresponding sides

Thus ,

$: \mapsto \tt \frac{Area \: of \: first \: \triangle }{Area \: of \: second \: \triangle} = { (\frac{3}{5} )}^{2}$

$: \mapsto \tt \frac{Area \: of \: first \: \triangle }{Area \: of \: second \: \triangle} = \frac{9}{25}$

Therefore ,

The ratio of areas of two similar Δ is 9 : 25