Question

The perimeters of two similar triangles are 30 cm and 20 cm respectively.
If one side of the first triangle is 9 cm long, find the length of the
corresponding side of the second triangle.​

Answer 1

AnswEr :

$\textbf{\underline{Given That :} Two Triangles are Similar}\\\\\textsf{Then the Ratio of Perimeters will be Equal}\\\textsf{to Ratio of Corresponding Sides of Triangles.}$

$\rule{170}{2}$

$\underline{\bigstar\:\textsf{According to the Question :}}$

$\dashrightarrow\tt\:\: \dfrac{Perimeter_{\tiny\triangle 1}}{Perimeter_{\tiny\triangle 2}}=\dfrac{Side_{\tiny\triangle 1}}{Side_{\tiny\triangle 2}}\\\\\\\dashrightarrow\tt\:\:\dfrac{30 \:cm}{20 \:cm} =\dfrac{9 \:cm}{Side_{\tiny\triangle 2}}\\\\\\\dashrightarrow\tt\:\:Side_{\tiny\triangle 2} = \dfrac{9 \:cm \times 20 \:cm}{30 \:cm}\\\\\\\dashrightarrow\tt\:\:Side_{\tiny\triangle 2} = \dfrac{180 \: {cm}^{2} }{30 \:cm}\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt Side_{\tiny\triangle 2} =6 \:cm}}$

⠀

$\therefore\:\underline{\textsf{Corresponding Side of 2nd triangle is \textbf{6 cm }long.}}$

Answer 2

||✪✪ QUESTION ✪✪||

The perimeters of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangle is 9 cm long, find the length of the corresponding side of the second triangle. ?

|| ★★ FORMULA USED ★★ ||

→ In two similar triangles The perimeters of the two triangles are in the same ratio as the sides.

→ The corresponding sides, medians and altitudes will all be in this same ratio.

|| ✰✰ ANSWER ✰✰ ||

Given that, perimeters of two similar triangles are 30 cm and 20cm and also one side of the first triangle is 9 cm,

Let us assume that, side of Second ∆ is x cm.

So , we can say that :-

→ ∆1 Perimeter / ∆2 Perimeter = (9/x)

→ (30/20) = (9/x)

→ (3/2) = (9/x)

Cross - Multiply,

→ 3x = 18

Dividing both sides by 3,

→ x = 6cm.

Hence, the length of the corresponding side of the second ttriangle is 6cm.

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❁❁ Also Remember ❁❁ :- If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

If we say that, ∆ABC is Similar to ∆PQR,

Than, we can say that :-

→ (Area ∆ABC) / (Area ∆PQR) = (AB/PQ)² = (BC/QR)² = (CA/RP)².

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