In a School, girls were asked to prepare Rangoli in triangular shape during the visit by Directorates of Education. Dimensions of the triangle were 52 cm, 56 cm and 60 cm. Find the area covered in the rangoli. Also find the length of the garland to be placed on the boundary of the rangoli. What values are depicted here?
Answers
Given :- In a School, girls were asked to prepare Rangoli in triangular shape during the visit by Directorates of Education. Dimensions of the triangle were 52 cm, 56 cm and 60 cm. Find the area covered in the rangoli. Also find the length of the garland to be placed on the boundary of the rangoli. What values are depicted here ?
Solution :-
we have , Dimensions of the triangle were 52 cm, 56 cm and 60 cm.
so,
→ Perimeter of ∆ = 52 + 56 + 60 = 168 m = The length of the garland to be placed on the boundary of the rangoli.
now,
→ semi - perimeter = 168/2 = 84 m
then,
→ Area of ∆ = √[s(s - a)(s - b)(s - c)] where s is semi - perimeter and a, b and c are length of sides of ∆.
so,
→ Area of ∆ = √[84 * (84 - 52) * (84 - 56) * (84 - 60)]
→ Area of ∆ = √[84 * 32 * 28 * 24]
→ Area of ∆ = √[12 * 7 * 8 * 4 * 7 * 4 * 8 * 3]
→ Area of ∆ = √[4 * 3 * 7² * 4² * 8² * 3]
→ Area of ∆ = √[2² * 3² * 4² * 7² * 8²]
→ Area of ∆ = 2 * 3 * 4 * 7 * 8
→ Area of ∆ = 1344 m².
Therefore, the area covered in the rangoli is 1344 m².
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