What is the length of larger side AB of roof?

Question

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?

$(U s e \sqrt 3 = 1.73)$

Smart Achievers · Accepted Answer

(4)

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

$I n △ A E D, r i g h t a n g l e d a t E, w e h a v e c o s ∠ D A E = \frac{A E}{A D} \Rightarrow c o s 30 ° = \frac{A E}{6} [∵ ∠ D A E = 30 ° and A D = 6 m] \Rightarrow \frac{\sqrt{3}}{2} = \frac{A E}{6} \Rightarrow A E = 3 \sqrt{3} m ∵ c o s 30 \circ = 32 A l s o, △ A D E ≅ △ B C F \Rightarrow A E = B F = 3 \sqrt{3} m Now, AB = AE + EF + BF = 3 \sqrt{3} + 8 + 3 \sqrt{3} [∵ DEFC is a rectangle \Rightarrow CD = EF = 8 m] = 6 \sqrt{3} + 8 = 6 \times 1.73 + 8 = 18.38 m$

Hence, length of larger side of roof is 18.38 m

Solution

1 17.35 m

2 15.5 m

3 13.5 m

4 18.38 m

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