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Question
The sides of a triangle are 16 cm, 12 cm, and 20 cm. Find :
(i) area of the triangle ;
(ii) height of the triangle, corresponding to the largest side ;
(iii) height of the triangle, corresponding to the smallest side.
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Solution
Sides of ∆ are
a = 20 cm
b = 12 cm
c = 16 cm
`S = (a + b + c)/2`
= `(20 + 12 + 16)/2`
= `48/2 = 24`
area of Δ = `sqrt(s(s - a)(s - b)(s - c))`
= `sqrt(24(24 - 20)(24 - 12)(24 - 16))`
= `sqrt(24 xx 4 xx 12 xx 8)`
= `sqrt(12 xx 2 xx 4 xx 12 xx 2 xx 4)`
= `sqrt(12 xx 12 xx 4 xx 4 xx 2 xx 2)`
= `12 xx 4 xx 2 = 96 "cm"^2`
AD is height of Δ corresponding to largest side.
∴ `1/2 xx "BC" xx "AD" = 96`
`1/2 xx 20 xx "AD" = 96`
AD = `(96 xx 2)/20`
AD = 9.6 cm
BE is height of Δ corresponding to smallest side.
∴ `1/2 "AC" xx "BE" = 96`
`1/2 xx 12 xx "BE" = 96`
BE = `(96 xx 2)/12`
BE = 16 cm
(i) 96 cm2 (ii) 9.6 cm (iii) 16 cm
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