Q9 of 99 Page 267

The ratio of the length of sides of a triangular park of our village is 2:3:4; perimeter of park is 216 meter.

(i) Let us write by calculating the area of the park.


(ii) Let us write by calculating how long is to be walked from opposite vertex of longest side to that side straightly.

Let the length of sides of a triangular park be x cm


Given, length of sides = 2x, 3x and 4x


Also perimeter of triangular park = 2x +3x+4x = 216(given)


⇒ 9x = 216


⇒ x = 24 cm


⇒ three sides of triangle are 2× 24 = 48cm, 3× 24 = 72cm and 4× 24 = 96cm


i) Area of Triangle =


And s = semi perimeter of the triangle


⇒


⇒


=168 cm


Area of triangular park =


=


=


= 11804.49cm2


ii) Distance is to be walked from opposite vertex of longest side to that side straightly


Here longest side is 96cm


The distance walked from the opposite vertex of longest side to that side straightly is perpendicular distance from the vertex to the longest side


This is the height of the triangular park (h)


Area of triangular park =


⇒


⇒


⇒


⇒ h = 245.93 cm


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(i) Let us write by calculating what will be the cost of planting grass in the triangular field at the rate of Rs. 5 per sq. meter.


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