Sides AB and BE of a right triangle, right angled at B are of lengths 16 cm and 8 cm
respectively. The length of the side of largest square FDGB that can be inscribed in the
triangle ABE is
(a) 32/3cm
(b) 16/3cm
(c)8/3cm
(d) 4/3cm
BOARD SAMPLE PAPER QUESTION
Answers
Given : Sides AB and BE of a right triangle, right angled at B are of lengths 16 cm and 8 cm respectively.
To Find : The length of the side of largest square FDGB that can be inscribed in the triangle ABE is
Solution:
Let say side of square FDGB = x cm
=> FD =x cm and BF = x cm
AF = AB - BF = 16 - x cm
ΔAFD ~ ΔABE using AA similarity
=> AF/AB = FD/BE
=> (16 - x)/16 = x / 8
=> 16 - x = 2x
=> 3x = 16
=> x = 16/3 cm
The length of the side of largest square FDGB that can be inscribed in the triangle ABE is 16/3 cm
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Options a is the correct option
