Question

Assertion: The sides of a triangle are in the ratio 5:12:13 and its perimeter is 150m then the area of the triangle is 750m². Reason: If 2s=(a+b+c),where a,b,c are the sides of a triangle , then Area of triangle=​

Answer 1

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