Question

The sides of a triangle are in the ratio 11:19:24 and its perimete is 540cm. Find the area of the triangle. ​

Answer 1

Let one side be 11x, second be 19x and third be 24x.

Perimeter = 540cm

11x + 19x + 24 x = 540

54x = 540

x = 540/54

x = 10

11*10=110 , 19 * 10 = 190 , 24*10 =240

Semiperimeter = 540/2 = 270

Area of triangle =

√s (s-a) (s-b) (s-c)

= √270 (270-110) (270-190) (270-240)

=√270 (160) (80) (30)

= √270 (160) (240)

=√270 . 38400

= √ 10368000

= √2.2.2.2.2.2.2.2.2.2.5.5.5.11

= 2.2.2.2.2.5 √5.11

= 160 √55 Sq . cm

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