Q11 of 62 Page 186

A boy is designing a diamond shaped kite, as shown in the figure where AE = 16 cm, EC = 81 cm. He wants to use a straight cross bar BD. How long should it be?

To find DB

Let ∠EAD = x ----(1)


⇒ ∠ADE = 90 – x (∵ AED = 90 and sum of angles of triangle is 180)


⇒ ∠EDC = x (∵ ∠ADC = 90) ----(2)


⇒ ∠EAD = ∠EDC (by (1) and (2)) ----(3)


Now,


In ΔAED and ΔDEC


∠AED = ∠DEC (both perpendicular to AC)


∠EAD = ∠EDC (by (3))


∴ ΔAED ∼ ΔDEC


(∵ ΔAED ∼ ΔDEC)


⇒ 16×81 = ED2


⇒ ED = 36 cm


⇒ 2×ED = DB = 72 cm


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