Question

the length of sides of traingle is 3:4:5 and its perimeter is 48 find its area
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Answer 1

✯Question✯

• The lengths of sides of triangle are in the ratio 3:4:5 and it's perimeter is 48cm. Find it's area.

✭Given✭

• Ratio of lengths of triangle = 3:4:5
• Perimeter = 48cm

✶To find✶

• Area of the triangle

✬Solution✬

• Let the sides of the triangle be 3x , 4x , 5x
• Perimeter = Sum of all sides
• 48cm = 3x + 4x + 5x
• 12x = 48cm
• x = ⁴⁸⁄₁₂
• x = 4

✭Substitution✭

• 3x = 3(4) = 12cm
• 4x = 4(4) = 16cm
• 5x = 5(4) = 20cm

★We got the sides of the triangle★

★By Heron's Formula, let's find area★

• Perimeter = 48cm
• Semi Perimeter = ⁴⁸⁄₂ = 24cm
• a = 12cm
• b = 16cm
• c = 20cm
• s = 24cm

✵Formula✵

• √s(s-a)(s-b)(s-c)
• √24(24-12)(24-16)(24-20)
• √24(12)(8)(4)
• √24(384)
• √9216
• 96cm²

✩The area of triangle is 96cm²✩