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Solution


Q.

A farmer had a triangular piece of land. He put a fence, parallel to one of the sides of the field as shown in the figure.

Based on the above information answer the following questions:

 

(ii) If AD = x + 1, DB = 3x – 1, AE = x + 3, EC = 3x + 4, then find the value of x.
1 7  
2 5  
3 4  
4 3  

Ans.

(1)

Given, AD = x + 1, DB = 3x – 1, AE = x + 3, EC = 3x + 4.

Since, in ΔABC, DE ∥ BCADDB=AEEC(Using BPT)x+13x-1=x+33x+4Cross multiplying:(x+1)(3x+4)=(3x-1)(x+3)3x2+7x+4=3x2+8x-37x+4=8x-3⇒x=7