Question

If the ratio of the area of 2 silimiliar
triangles are 121 : 49 then find the
ration of their corresponding sides.​

Answer 1

AnswEr

Given ratio of the area of 2 silimiliar triangles is 121 : 49.

We've to find ratio of their corresponding sides.

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⠀⠀⠀

$\star$ Ratio of areas of two similar triangles is equal to the ratio of the squares of the corresponding heights.

$\longrightarrow\sf \dfrac{Area_{(1)}}{Area_{(2)}} = \dfrac{Side_{1}}{Side_{(2)}}$

Now, squaring ratio of the areas of both Traingle :

$\longrightarrow\sf Ratio = \dfrac{121}{49} \\\\\\\longrightarrow\sf Ratio = \Bigg(\dfrac{11}{7} \Bigg)^2 \\\\\\\longrightarrow\boxed{\frak{\purple{Ratio = \dfrac{11}{7}}}}$

$\therefore$ Ratio of their corresponding side is $\sf 11/7.$

Answer 2

Given ratio of the area of 2 silimiliar triangles is 121 : 49.

We've to find ratio of their corresponding sides.

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Ratio of areas of two similar triangles is equal to the ratio of the squares of the corresponding heights.

\longrightarrow\sf \dfrac{Area_{(1)}}{Area_{(2)}} = \dfrac{Side_{1}}{Side_{(2)}}⟶

Area

(2)

Area

(1)

=

Side

(2)

Side

1

Now, squaring ratio of the areas of both Traingle :

\begin{gathered}\longrightarrow\sf Ratio = \dfrac{121}{49} \\\\\\\longrightarrow\sf Ratio = \Bigg(\dfrac{11}{7} \Bigg)^2 \\\\\\\longrightarrow\boxed{\frak{\purple{Ratio = \dfrac{11}{7}}}}\end{gathered}

⟶Ratio=

49

121

⟶Ratio=(

7

11

)

2

⟶

Ratio=

7

11

\therefore∴ Ratio of their corresponding side is \sf 11/7.11/7.