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Question
Use the information given in the adjoining figure to find :
(i) the length of AC.
(ii) the area of an ∆ABC
(iii) the length of BD, correct to one decimal place.
Solution
AB = 24 cm, BC = 7 cm
(i)
AC = `sqrt("AB"^2 + "BC"^2)`
= `sqrt(24^2 + 7^2)`
= `sqrt(576 + 49)`
= `sqrt(625) = 25` cm
(ii)
Area of ΔABC = `1/2 "AB" xx "BC"`
= `1/2 xx 24 xx 7 = 84` cm2
(iii)
BD ⊥ AC
Area ΔABC = `1/2 "AC" xx "BD"`
`84 = 1/2 xx 25 xx "BD"`
⇒ BD = `(84 xx 2)/25 = 168/25 = 6.72` cm
= 6.72 cm ≈ 6.7 cm
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