Question

The three sides of a triangle are in the ratio 2 : 3 : 4 and the perimeter 225 m. Find its area

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• Three sides of ∆s are 2:3'4
• perimeter is 225m

${\sf{\green{\underline{\large{To\:find}}}}}$

• Its area

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Diagram

$\setlength{\unitlength}{5mm}\begin{picture}(5,5)\put(0,0){\line(1,0){8}}\put(0,0){\line(2,1){6}}\put(8,0){\line(-2,3){2}}\end{picture}$

Solution

Let the side of ∆ be x

Then sides are

2x ,3x and 4x

=>2x+3x+4x=225

=>9x=225

=>x=25

Here sidea will be 2x =50 ,3x = 75 and 4x=100

Area of ∆

=>(a+b+c)/2

=>(50+75+100)/2

=>225/2

$\tt\sqrt{S(S-A)(S-B)(S-C)]}$

Putting the value

$\tt\sqrt{S(S-A)(S-B)(S-C)]}$

See the attachment

=1875√15

Answer 2

Answer:

27967m^2 ( approx.)

Step-by-step explanation:

Given : Sides of triangle are in ratio of 2:3:4

Perimeter of triangle : 225m

To find : Area of triangle

Solution : Perimeter of triangle : 225m

Sum of all sides = 225

let the sides be 2x , 3x and 4x respectively

2x+3x+4x = 225

9x = 225

x = 225/9

x = 25

Therefore, the sides are

2x = 2(25) = 50m

3x = 3(25) = 75m

4x = 4(25) = 100m

Area of triangle = 1/2(base)(height)

But we don't know what is base and what is height.

Therefore, the area of triangle = √s(s-a) (s-b) (s-c)

here s = a+b+c/2 = Perimeter / 2

=225/2 = 112.5

a, b and c are sides.

so,

Area = √112.5(112.5-100)(112.5-75)(112.5-50)

= √ 112.5(1.125)(37.5)(62.5)

=27966.62

=27967m^2 (approx.)

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NaVila11

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