Question

the sides of a triangle are in the ratio 11:19:24 and its perimeter is 540cm find the area of the triangle​

Answer 1

Answer:

= 7200√2 cm2

Step-by-step explanation:

Ratio of the sides of the triangle = 11 : 19 : 24

Let the common ratio be x then sides are 11x, 19x and 24x

Perimeter of the triangle = 540cm

11x + 19x + 24x = 540 cm

⇒ 54x = 540cm

⇒ x = 10

Sides of triangle are

11x = 11 × 10 = 110cm

19x = 19 × 10 = 190cm

24x = 24 × 10 = 240cm

Semi perimeter of triangle(s)

= 540/2 = 270cm

Using heron's formula,

Area of the triangle

= √s (s-a) (s-b) (s-c)

= √270(270 - 110) (270 - 190) (270 - 240)cm2

= √270 × 160 × 80 × 30

= 7200√2 cm2

Answer 2

Answer:

area of the triangle is 10,450cm2

Step-by-step explanation:

let the sides of the triangle be 11x,19x,24x

then

sum of all the sides of a triangle = perimeter

11x+19x+24x = 540

54x = 540

x= 540/54

x = 10cm

Now the sides of the triangle are 110cm, 190cm, 240cm

hypotenuse = 240cm, base = 110cm, height = 190cm

area = 1/2× base × height

1/2×110×190 = 10,450