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SHUBHAM SHEKHAR

· started a discussion

· 1 Months ago

Wrong method of solution (Question: 111672.0 )

Using a different method I have got a different answer.

Question:
A rectangular plank \(\sqrt[]{2}\)m wide is placed symmetrically on the diagonal of a square of side 8 m as shown in the figure. The area of the plank is:


Options:
A)

\(\big( 16\sqrt[]{2}-3 \big)\)sq.m

B) 7\(\sqrt[]{2}\) sq. m
C) 98 sq.m
D) 14 sq.m
Solution:
Ans: (d)


Here EG = EH = \( \cfrac{\sqrt{2}}{2}=\cfrac{1}{\sqrt{2}}\)

From \(\Delta\)HAG,

tan \(45^o=\cfrac{AE}{EG}\)

or \(1=\cfrac{AE}{\cfrac{1}{\sqrt{2}}}\)

 \( \therefore\) AE = \(\cfrac{1}{\sqrt{2}}\)

Also,  AC = \(\sqrt{8^2+8^2}=\sqrt{128}=8\sqrt{2}\)

So that EF = AC - 2AE  = \(8\sqrt{2}-2\times\cfrac{1}{\sqrt{2}}\)

= \(8\sqrt{2}-\sqrt{2}=7\sqrt{2}\)

Hence area of plank = HG x EF = \(\sqrt[1]{2}\times7\sqrt{2}=14\) sq.m

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