Q. 164.5( 2 Votes )

A right angle triangle has AOB =90°, AC = BC, OA = 12 cm and OC = 6.5 and OB is its base. Find the measure of OB.

Answer :

We have



Given: ∆AOB is a right-angled triangle, right angled at O.


AC = BC


C is the mid-point of AB.


OA = 12 cm


OC = 6.5 cm


Now the mid-point of the hypotenuse of a right triangle is equidistant from the vertices.


Therefore, AC = BC = OC


AC = BC = 6.5 cm [ OC = 6.5cm]


Now, AB = AC + BC [ C is the midpoint of AB]


AB = 6.5 + 6.5


AB = 13 cm


According to Pythagoras theorem in ∆AOB,


AO2 + OB2 = AB2


OB2 = AB2 - AO2


OB2 = 132 - 122


OB2 = 169 - 144


OB2 = 25


OB = √25 = 5 cm


Thus, OB = 5 cm.


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