Q5 of 95 Page 5

Find the length of a diagonal of a rectangle whose adjacent sides are 30 cm and 16 cm.


Let ABCD be a rectangle and AB and BC are the adjacent sides of length 30cm and 16cm respectively.


Let AC be the diagonal.


In ∆CBA, using Pythagoras Theorm,


(Perpendicular)2 + (Base)2 = (Hypotenuse)2


⇒ (AB)2 + (BC)2 = (AC)2


⇒ (30)2 + (16)2 = (AC)2


⇒ (AC)2 = 900 + 256


⇒ (AC)2 = 1156


⇒ AB = ±34


⇒ AB = 34 [taking positive square root]


Hence, the length of a diagonal of a rectangle is 34cm


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