Question

the sides of a triangle are in the ration 3:4:5 . if its perimeter is 36. then what is its area​

Answer 1

Answer:

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Answer 2

Answer:

Given,

Perimeter = 36

Let the ratio be x.

Therefore,

$= AB + BC + CA = 36$

$=3x+4x+5x=36$

$=12x=36$

$= x= \frac{36}{12}$

$=x=3$

Now, putting the value of x.

$AB=3x=9cm$

$BC=4x=12cm$

$AC=5x=15cm$

On using Pythagoras theorem,

$AC^{2} = AB ^{2} +BC^{2}$

$= 9^{2} + 12^{2}$

$=81+144$

$= AC^{2} =225$

$= AC = 15cm$

Δ ABC is a right angled triangle and ∠B is the right angle.

Area of Δ ABC = $\frac{1}{2} AB$ × $BC$ $= \frac{1}{2}$ × 9 × 12 = $54^{2}$

Answer: The area of the triangle is $54^{2}$.