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Question

In the given figure, DEBC.
(i) If AB=x,BD=x+2 and EC=x1, find the value of x.
(ii) If DB=x3,AB=2x,EC=x2 and AC=2x+3, find the value of x.

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Solution

(i) From the figure, it is given that,
Consider the ABC,
AD/DB=AE/EC
x/(x2)=(x+2)/(x1)
By cross multiplication we get,
X(x1)=(x2)(x+2)
x2x=x24
x=4
x=4
(ii) From the question it is given that,
DB=x3,AB=2x,EC=x2 and AC=2x+3
Consider the ABC,
AD/DB=AE/EC
2x/(x2)=(2x+3)/(x3)
By cross multiplication we get,
2x(x2)=(2x+3)(x3)
2x24x=2x26x+3x9
2x24x2x2+6x3x=9
7x+6x=9
x=9
x=9.

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