Question

The sides of a right-angled triangle are in the ratio 3:4:5 and the area of the triangle is 96 cm² . The length of the largest side of the triangle is _____ ?​

Answer 1

Answer:

Let the sides of triangles are 3x,4x and 5x.

And perimeter of the triangle is 144cm.

So , 3x+4x+5x=144

12x=144

x=12

so, the sides are triangle are 3(12)=36cm, 4(12)=48cm , 5(12)=60cm

so , the longest side is 60 cm.

Area of triangle =

s(s−a)(s−b)(s−c)

here , s=72 and a=36, b=48 c=60

=

72(72−36)(72−48)(72−60)

=

72(36)(24)(12)

=

746496

= 864

So, the area of triangle is 864 cm

2

and the height corresponding to longest side h=

60

2×864

=28.8cm

Answer 2

Answer:

Let the sides of triangles are 3x,4x and 5x.

And perimeter of the triangle is 144cm.

So , 3x+4x+5x=144

       12x=144

         x=12

so, the sides are triangle are 3(12)=36cm, 4(12)=48cm , 5(12)=60cm

so , the longest side is 60 cm.

Area of triangle =  

s(s−a)(s−b)(s−c)

​

 

here , s=72 and a=36, b=48 c=60

                          =  

72(72−36)(72−48)(72−60)

​

 

                           =  

72(36)(24)(12)

​

 

                            =  

746496

​

 

                             = 864

So, the area of triangle is 864 cm  

2

 and the height corresponding to longest side h=  

60

2×864

​

=28.8cm

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