20. Least Common Multiple (LCM) of three numbers which are in the ratio 3:4: 5 is 720. If a triangle has these three numbers as its length of sides (in cm) and P (cm) is the perimeter and A (sq. cm.) is the area of the triangle; then find by what percentage numerically A is more than P? 3 : 4 : 5 నిష్పత్తిలో ఉన్న మూడు సంఖ్యల కనిష్ట సామాన్య గుణిజము (క.సా.గు.) 720. ఈ మూడు సంఖ్యలు ఒక త్రిభుజము యొక్క భుజముల కొలతలు (సె.మీ.) అయి, P త్రిభుజము చుట్టుకొలత మరియు A ఆ త్రిభుజము యొక్క వైశాల్యం అయితే, సంఖ్యాత్మకంగా P కంటే, A ఎంత శాతం ఎక్కువ ?

 

Let’s solve the question step-by-step in easy and copyable format.

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🔹 Given:

• Three numbers are in ratio 3 : 4 : 5
• Their LCM = 720
• These represent the sides of a triangle
• We are to find by what percentage the area (A) is more than perimeter (P)

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Step 1: Let the three numbers be

3x, 4x, 5x

Then,

LCM of 3x, 4x, 5x = LCM of x × LCM(3, 4, 5) = x × 60

Given: LCM = 720
So,

x × 60 = 720 → x = 12

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Step 2: Sides of triangle

3x = 36 cm  
4x = 48 cm  
5x = 60 cm

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Step 3: Perimeter (P)

P = 36 + 48 + 60 = 144 cm

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Step 4: Area (A)

This is a right-angled triangle (3-4-5 type), so use:

Area = (1/2) × base × height  
→ (1/2) × 36 × 48 = 864 sq. cm

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Step 5: % by which Area is more than Perimeter

We compare A and P:

A = 864  
P = 144

Find percentage more:

% more = ((A - P)/P) × 100  
       = ((864 - 144)/144) × 100  
       = (720 / 144) × 100 = 5 × 100 = 500%

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✅ Final Answer: Area is 500% more than Perimeter ✅

Let me know if you want it in Telugu too.