Sides AB And BE of a Right Triangle, Right Angled At B Are of Lengths 16 Cm And 8 Cm Respectively ~ Mathematics

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

(b) 16/3cm

Explanation:

△ ABE is right triangle and FDGB is a square of side x

∴ △ ABE ~△ DGE  (AA)

= `"AF"/"DG"` = `"FD/GE"` (CPST)

= `"16 - x"/"x"` = `"x"/"8-x"`

= (16 - x) (8 - x) = `x^{2}`

= 16 (8 - x) -x (8 - x) = `x^{2}`

= 128 - 16x - 8x = 0

= 128 - 24x = 0

= 128 = 24x

= 24x = 128

= x = `128/24`

∴ x= `16/3`

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