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.

Answer 1

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