∆LMN ~ ∆PQR, 9 × A(∆PQR) = 16 × A(∆LMN). If QR = 20, then fi

1.	∆LMN ~ ∆PQR, 9 × A(∆PQR) = 16 × A(∆LMN). If QR = 20, then find MN.
Answer» 9 × A(∆PQR) = 16 × A(∆LMN) [Given] ∴ (ΔLMN)/A(PQR) = 9/16 (i) Now, ∆LMN ~ ∆PQR [Given] ∴ (ΔLMN)/A(PQR) = MN²/QR² (ii) [Theorem of areas of similar triangles] ∴ MN²/QR²= 9/16 [From (i) and (ii)] ∴MN = QR = 3/4 [Taking square root of both sides] ∴ MN/20 = 3/4 ∴ MN = (20 x 3)/4 ∴ MN = 15 units

∆LMN ~ ∆PQR, 9 × A(∆PQR) = 16 × A(∆LMN). If QR = 20, then find MN.

Answer»

9 × A(∆PQR) = 16 × A(∆LMN) [Given]

∴ (ΔLMN)/A(PQR) = 9/16 (i)

Now, ∆LMN ~ ∆PQR [Given]

∴ (ΔLMN)/A(PQR) = MN²/QR² (ii) [Theorem of areas of similar triangles]

∴ MN²/QR²= 9/16 [From (i) and (ii)]

∴MN = QR = 3/4 [Taking square root of both sides]

∴ MN/20 = 3/4

∴ MN = (20 x 3)/4

∴ MN = 15 units

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∆LMN ~ ∆PQR, 9 × A(∆PQR) = 16 × A(∆LMN). If QR = 20, then find MN.

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