Question

A figure is in the form of a quadrilateral ABCD its
area is 165 cm. Find the length of the perpendicular
drawn from D on AC if AC =15 cm and length of
perpendicular from B on AC is 12 cm.​

Answer 1

the length of the perpendicular drawn from D on AC = 10 cm

Step-by-step explanation:

Area of Δ ACD = (1/2) AC * (the length of the perpendicular drawn from D on AC)

Area of of Δ ABC = (1/2) AC * (the length of the perpendicular drawn from BD on AC)

= (1/2) * 15 * 12

= 90 cm²

Area of Δ ACD  + Area of of Δ ABC = Area of Quadrilateral ABCD

=> Area of Δ ACD  + 90 = 165

=> Area of Δ ACD = 75 cm²

(1/2) 15 * (the length of the perpendicular drawn from D on AC) = 75

=> the length of the perpendicular drawn from D on AC = 10 cm

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