In the Rangoli competition, the students are asked to prepare a Rangoli in triangular shape. Dimensions of △PQRare 28 cm, 26 cm and 18 cm. The winner team has decorated Rangoli with the flower petals in the △LMN asshown in the figure, where L, M and N are the midpoints of sides PQ, PR and QR respectively. Find the area of△LMN (√10=3.16)
Answers
Solution :-
Side of ∆PQR are 28 cm, 26 cm and 18 cm .
So,
→ Semi - perimeter of ∆PQR = s = (18 + 26 + 28)/2 = 36
now, using heron's formula to find the area of ∆PQR,
→ Area (∆PQR) = √[s * (s - a) * (s - b) * (s - c)]
→ Area (∆PQR) = √[36 * (36 - 28) * (36 - 26) * (36 - 18)]
→ Area (∆PQR) = √[36 * 8 * 10 * 18]
→ Area (∆PQR) = √[2 * 8 * 18 * 18 * 10]
→ Area (∆PQR) = 4 * 18√10
→ Area (∆PQR) = 72 * 3.16 { given that, √10 = 3.16 }
→ Area (∆PQR) = 227.52 cm²
therefore,
→ ∆LMN area = (1/4) * Area (∆PQR) { since , ∆ is formed by joining the mid points. }
→ ∆LMN area = (1/4) * 227.52
→ ∆LMN area = 56.88 cm² (Ans.)
Hence, the area of ∆LMN is equal to 56.88 cm² .
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