Question

the altitude of two similar triangles are 30 cm and 20 cm respectively . if one side of first triangle is 12 cm then determine corresponding side of second triangle​

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• Two similar ∆s
• ∆ABC and ∆PQR
• where Altitude of AD=30cm and PS =20
• If AB=12

${\sf{\green{\underline{\large{To\:find}}}}}$

• Corresponding sides

${\sf{\pink{\underline{\Large{Explanation}}}}}$

☞ ∆ABC ~ ∆PQR

$\rightarrow\tt\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$

From Theorm

• Sides of similar ∆ is proportional
• to its Altitude
• or angle bisector Side

Therefore From this Theorm

$\rightarrow\tt\frac{AD}{PS}$

$\rightarrow\tt\frac{AD}{PS}=\frac{30}{20}$

$\rightarrow\tt\frac{AD}{PS}=\cancel{\frac{30}{20}}$

$\rightarrow\tt\frac{AD}{PS}=\frac{3}{2}$

Now

$\rightarrow\tt\frac{AD}{PS}=\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$

$\rightarrow\tt\frac{3}{2}=\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$

$\rightarrow\tt\frac{3}{2}=\frac{12}{PQ}$

PQ=8

Hence values of PQ =8

Answer 2

Aɴꜱᴡᴇʀ

☞ PQ = 8 cm

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Gɪᴠᴇɴ

➢ Altitude of 2 similar triangles are 30 cm and 20 cm

➢ One side of the first triangle is 12 cm

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Tᴏ ꜰɪɴᴅ

☆ Corresponding side of the other triangle?

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Sᴛᴇᴘꜱ

❍ Let us assume that the two triangles are ∆ABC and ∆PQR

We know that in similar ∆s

• Sides of similar triangles are proportional to its altitude or angle bisector

• Corresponding sides are of the same ratio.

That is,

$\underline{\boxed{\sf{\green{\dfrac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}}}}}$

$\dashrightarrow\sf\dfrac{AD}{PS}$

$\leadsto\sf\dfrac{AD}{PS}=\dfrac{30}{20}$

$\leadsto\sf\dfrac{AD}{PS}=\cancel{\dfrac{30}{20}}$

$\leadsto\sf\dfrac{AD}{PS}=\dfrac{3}{2}$

$\leadsto\sf\dfrac{AD}{PS}=\dfrac{AB}{PQ}=\dfrac{BC}{QR}=\dfrac{AC}{PR}$

$\leadsto\sf\dfrac{3}{2}=\dfrac{AB}{PQ}=\dfrac{BC}{QR}=\dfrac{AC}{PR}$

$\leadsto\sf PQ = \dfrac{3}{2}=\dfrac{12}{PQ}$

$\leadsto\sf\dfrac PQ = {12\times2}{3}$

$\sf\pink{ \leadsto PQ = 8 cm}$

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