Question

The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the height corresponding to the longest side.​

Answer 1

Answer:

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