the length of side of a triangle are int the ratio 4:5:3 and it perimeter is 96cm find it area
Answers
Answer:
384 cm²
Step-by-step explanation:
Let the sides of the triangle be 4x cm, 5x cm and 3x cm.
It is given that the perimeter of the triangle is 96 cm.
Therefore,
→ 4x + 5x + 3x = 96
→ 12x = 96
→ x = 96/12
→ x = 8
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Now, the sides of the triangle are :
1st side = a = 4x = 4(8) = 32 cm
2nd side = b = 5x = 5(8) = 40 cm
3rd side = c = 3x = 3(8) = 24 cm
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Let's find out if the triangle is a right - angles triangle or not.
It can be find out using Pythagoras Theorem.
→ (Hypotenuse)² = (Base)² + (Perpendicular)²
Let, the bigger side be hypotenuse and the other two sides be base and perpendicular.
→ (40)² = (32)² + (24)²
→ 1600 = 1024 + 576
→ 1600 = 1600
Hence, the triangle is a right - angles triangle.
Applying formula :
Area of triangle = 1/2 × Base × Perpendicular
→ 1/2 × 32 × 24
→ 32 × 12
→ 384 cm²