Question

in the rangoli competition the students were asked to prepare a rangoli in triangular shape dimensions of triangle pqr and 28cm 26cm and 18cm the winner team has decorative Rangoli with the flower petals in the triangle lmn as shown in the figure where l m n are the midpoints of sides PQ PR and QR respectively find the area of the the triangle lmn ( root 10 =3.16)




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Answer 1

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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