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Question
In a ∆ABC, if a = 18 cm, b = 24 cm and c = 30 cm, then show that its area is 216 sq.cm
Solution
In a ∆ABC,
Given a = 18 cm, b = 24 cm and c = 30 cm
S = `("a" + "b" + "c")/2`
= `(18 + 24 + 30)/2`
= `7/2`
= 36
Area of the triangle ABC
∆ = `sqrt("s"("s" - "a")("s" - "b")("s"- "c"))`
∆ = `sqrt(36(36 - 18)(36 - 24)(36 - 30))`
∆ = `sqrt(36 xx 18 xx 12 xx 6)`
= `sqrt(6 xx 6 xx 3 xx 6 xx 2 xx 6 xx 6)`
= `sqrt(6^2 xx 6^2 xx 3 xx 2 xx 6)`
= `sqrt(6^2 xx 6^2 xx 6^2)`
= 6 × 6 × 6
= 216 sq.cm
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