Question

The sides of a triangle are in the ratio 3 : 4 : 5. if it's perimeter is 300 cm, find its area

Answer 1

Answer:

perimeter=36

let the ratio be x

therefore,

⇒AB+BC+CA=36

⇒3x+4x+5x=36

⇒12x=36

⇒x=

12

36

⇒x=3

Now, putting the value of x

AB=3x=9cm

BC=4x=12cm

AC=5x=15cm

On using Pythagoras theorem

AC

2

=AB

2

+BC

2

=(9)

2

+(12)

2

=81+144

AC

2

=225

AC=15cm

ΔABC is right angled triangle ∠B is right angle.

Area of

ΔABC=

2

1

AB×BC

=

2

1

×9×12

=54cm

2

hence,

Area of triangle is 54cm

2

Step-by-step explanation:

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Answer 2

Let the number be 3x,4x and 5x

A/C :

3x+4x+5x = 300

=> 12x = 300

=> x = 300/12

=> x = 25

Now, Side = 3x = 3×25 = 75°; 4x = 4×25 = 100°;

5x = 5× 25 = 125°

Area =

1/4√-a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4

=1/4√﹣75⁴+2·(75·100)²+2·(75·125)²﹣100⁴+2·(100·125)²﹣125⁴

=3750cm²

Therefore, The area of the triangle is 3750cm²