Question

the sides of a triangle are in the ratio 3:4:5 and its perimeter is 24 cm. Find the area of the triangle​

Answer 1

$\sf{\huge{\underline{\purple{Given :-}}}}$

• The sides of a triangle are in the ratio 3:4:5.

• The perimeter is 24 cm.

$\sf{\huge{\underline{\pink{To\:Find :-}}}}$

• The area of the triangle.

$\sf{\huge{\underline{\blue{Solution :-}}}}$

Let, The given ratio of the measure of the sides be x then,

Then, the sides be 3x cm, 4x cm and 5x cm

Perimeter of the triangle = 24 cm (given)

We know , The Perimeter of the triangle = a + b + c

➝ a + b + c = 24

➝ 3x + 4x + 5x = 24

➝ 12x = 24

➝ x = 2

Thus, the sides are,

3x = 3 × 2 cm = 6 cm

4x = 4 × 2 cm = 8 cm

5x = 5 × 2 cm = 10 cm

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Let , the altitude AD ,

BD = DC = 5cm

Now , in Δ ADC,

AC² = AD² + DC²

➝ 8² = AD² + 5²

➝ AD² = 8² + 5²

➝ AD² = 64 + 25

➝ AD² = 89

➝ AD = √89 cm

➝ AD = 9.44 cm

We , know the area of traigle is

➝ ½ × b × h

➝ ½ × 5 × 9.44

➝ 5 × 4.72

➝ 23.59 cm²

The area of the triangle is 23.59 cm² .

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