Question

side of a triangle in rato 5:12:13 and its perimeter is 150 . the area of traingle

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Answer 1

Answer:

$750 m^{2}$ is your answer.

Step-by-step explanation:

The perimeter of triangle =150m (given)

Let the sides of the triangle be a, b and c, and "x" be the common ratio  

On dividing 150 m in the ratio 5:12:13, we get

a=5x m

b=12x m

c=13x m

We know that, the perimeter of a triangle = Sum of all sides =a+b+c

150=5x+12x+13x

150=30x

x=5

Sides are:

a=5x = 25 m

b=12x = 60 m

c=13x = 65 m

Now,

Let a, b, and c be the sides of a triangle.

Apply Heron's Formula to find the area of the triangle.

Area =  $\sqrt{S(S-a)(S-b)(S-c)}$

​  Where S =  $\frac{a+b+c}{2}$

​              S = $\frac{25+60+65}{2}$

                = 75 m

Area =  $\sqrt{(75(75-20)(75-60)(75-65))}$

        =  $\sqrt{(75*50*15*10)}$

        = $750 m^{2}$

The area of the triangle is $750 m^{2}$ .

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Answer 2

Step-by-step explanation:

9th

Maths

Heron's Formula

Heron's Formula

The sides of a triangle are...

Maths

The sides of a triangle are in the ratio 5:12:13, and its perimeter is 150 m. Find the area of the triangle.

Medium

Answer

Perimeter of triangle =150m (given)

Let the sides of triangle be,a, b and c,

On dividing 150 m in the ratio 5:12:13, we get

a=5xcm

b=12xcm

c=13xcm

we know that, perimeter of a triangle = Sum of all sides =a+b+c

150=5x+12x+13x

150=30x

x=5

Sides are:

a=5x=25cm

b=12x=60cm

c=13x=65cm

Now,

Let a, b and c be the sides of a triangle.

Apply Heron's Formula of find the area of triangle.

Area =

S(S−a)(S−b)(S−c)

Where S=

2

a+b+c

S=

2

1

(25+60+65)=75cm

Area =

(75(75−20)(75−60)(75−65))

=

(75×50×15×10)

=750

Area of triangle is 750cm

2

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