Question

From a point in the interior of an equilateral triangle perpendicular drawn to the three of are 8cm,10cm,and 11cm, respectively. Find the area of the triangle​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

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Step-by-step explanation:

see in figure O is a interior point of equilateral ∆PQR . where , three perpendiculars are x = 8 cm

y = 10 cm and z = 11 cm

because ∆PQR is an equilateral triangle

so, PQ = QR = RS = L ( let )

now,

area of ∆POR = 1/2 × OU × PR

ar∆PQR = 1/2 × y × L

ar∆PQR = 1/2× 10 × L = 5L

similarly,

area of ∆POQ = 1/2×OS × PQ

ar∆POQ = 1/2 × x × L

ar ∆PQQ = 1/2×8× L = 4L

area of ∆QOR =1/2×OT × QR

ar∆QOR = 1/2× z × L

ar∆QOR = 1/2×11× L = 11L/2

now,

area of ∆PQR = ar∆POQ + ar∆POR + ar∆QOR

√3/4 × side length² = 5L + 4L + 5.5L

√3/4 L² = (14.5)L

√3/4 L = 14.5

L = 14.5×4/√3 = 58/√3 cm

hence,

area of ∆PQR = √3/4 ×(58/√3)²

= √3/4 × 58²/3 cm²

= 29²/√3 cm²

= 485.56 cm²