Question

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

Answer 1

Answer:

It is given that the perimeter of the triangle is 144 cm. The value of x is 12. It means the length of sides are 36,48,60. The area of triangle is 864 cm

Answer 2

Step-by-step explanation:

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

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

$A = \sqrt{s} (s - a) \: (s - b)( s-c ) \\ where \:s = \frac{a + b + c}{2}$

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

The Area Of Triangle Is

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

The area of triangle is 864 cm².

The area of triangle is 864 cm².The area of triangle is

$A = \frac{1}{2} \times base \times \: height \\ 864 = \frac{1}{2} \times 60 \times height$

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

The height corresponding to the longest side is 28.8 cm.