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Solution


Q.

Riya and her sister visited their friend’s farmhouse. Upon arrival, Riya noticed that the roof of her friend’s house was shaped like a trapezium, with the dimensions indicated in the figure..

On the basis of above information, answer the following questions:

 

(iii) (a) What is the length of larger side AB of roof

  (Use √3 = 1.73)
1 17.35 m  
2 15.5 m  
3 13.5 m  
4 18.38 m  

Ans.

(4)

We have to find the length of larger side of roof i.e., AB.

In △AED, right angled at E, we havecos ∠DAE=AEAD⇒cos30°=AE6∵∠DAE=30° and AD=6 m⇒32=AE6⇒AE=33 m∵cos30∘=32Also, △ADE ≅ △BCF⇒AE=BF=33 mNow,AB=AE+EF+BF=33+8+33∵DEFC is a rectangle ⇒CD=EF=8 m=63+8=6×1.73+8=18.38 m

Hence, length of larger side of roof is 18.38 m