Question

6. The lengths of the sides of a triangle are in the ratio of 3:4:5 and its
perimeter is 14cm. Find the area of the triangle?
tell the steps also
pls help​

Answer 1

Answer:

The area of triangle is 864 cm² and the height corresponding to the longest side is 28.8 cm.

Step-by-step explanation:

The length of the sides of a triangle are in the ratio 3:4:5. Let the length of sides be 3x,4x,5x.

It is given that the perimeter of the triangle is 144 cm.

3x+4x+5x=1443x+4x+5x=144

12x=14412x=144

x=12x=12

The value of x is 12. It means the length of sides are 36,48,60.

Using heron's formula the area of triangle is

A=\sqrt{s(s-a)(s-b)(s-c)}A=

s(s−a)(s−b)(s−c)

Where,

s=\frac{a+b+c}{2}s=

2

a+b+c

s=\frac{144}{2}=72s=

2

144

=72

The area of triangle is

A=\sqrt{72(72-36)(72-48)(72-60)}=864A=

72(72−36)(72−48)(72−60)

=864

The area of triangle is 864 cm².

The area of triangle is

A=\frac{1}{2}\times base \times heightA=

2

1

×base×height

864=\frac{1}{2}\times 60 \times height864=

2

1

×60×height

height=\frac{864}{30}=28.8height=

30

864

=28.8

The height corresponding to the longest side is 28.8 cm.

or you can learn from this image