Question

if the ratio of three sides of triangle are 4:5:6.if the perimeter of triangle is 30m.find the area of triangle​

Answer 1

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Answer 2

Solution

Given :-

• If the ratio of three sides of triangle are 4:5:6
• the perimeter of triangle is 30m.

Find :-

• Area of triangle

Explanation

Let,

• First side = 4x
• Second side = 5x
• Third side = 6x

Using Formula

★ Perimeter of triangle = Sum of all side

★ Semi perimeter = (Sum of all side)/2

★ Area of triangle = √[S(S-AB)(S-BC)(S-CA)]

So,

➡ Perimeter of triangle = 4x + 5x + 6x

➡30 = 15x

➡x = 30/15

➡x = 2

Since

• First side = 4x = 4 × 2 = 8 m
• Second side = 5x = 5 × 2 = 10 m
• Third side = 6x = 6 × 2 = 12 m

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Now,calculate Semi perimeter.

➡ Semi perimeter (S) = (8+10+12)/2

➡ Semi perimeter (S) = 30/2

➡ Semi perimeter (S) = 15 m

Let,

ABC be a triangle ,

Where

• AB = 8 m
• BC = 10m
• CA = 12m

Now, Calculate area ,

➡Area = √[15(15-8)(15-10)(15-12)]

➡Area = √[15(7×5×3)]

➡Area = √[5 ×5 × 3 × 3 × 7]

➡Area = (5×3)√7

➡Area = 15√7 m²

Hence

• Area of triangle will be = 15√7 m²

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