Question

The perimeter of a triangle is 144 m and the ratio of the sides is 3: 4: 5. Find the area of
the triangle

Answer 1

Answer:

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Step-by-step explanation:

Given ratio = 3 : 4 : 5 .

Let the sides be 3x , 4x , 5x .

Given perimeter = 3x + 4x + 5x

= 12x = 144 m

= x= 144 / 12

= x = 12m .

Sides are 36 (3×12) , 48 (4×12) , 60 (5×12) m.

Now, Semiperimeter = 144/2 = 72 .

Area

= √ 72 × (72 - 36 ) × (72 - 48) × (72 -60)

= √ 72 × 36 × 24 × 12

= √ 746496

= 864 m

Therefore, Area = 864 m²

Answer 2

Given - 3:4:5

let side of a triangle be x. So the given sides will be 3x, 4x, 5x.

We know that ,

Perimeter => 3x+4x+5x = 144

=> 12x = 144 m

=> x = $\frac{144}{12}$

=> x = 12 m

Sides are :-

● 36(3×21)

● 48(4×12)

● 60(5×12)

Here, we get the semiperimeter = $\frac{144}{2}$

Area of the triangle will be,

$a = \sqrt{72 \times (72 - 36) \times (72 - 48) \times (72 - 60)} \\ = > a = \sqrt{72 \times 36 \times 24 \times 12} \\ = > a = \sqrt{746496} \\ = > a = 864m$

Hence the total area of the triangle is 864m.