Q1 of 21 Page 64

In the picture, the square on the hypotenuse of the top most right triangle is drawn.

Calculate the area and the length of a side of the square .



Applying Pythagoras Theorem for right – angled triangle,


Base2 + Perpendicular2 = Hypoteneous2


Which gives us in following right – angled triangles: –


In Δ BAD,


BA⊥ AD


⇒ BA2 + AD2 = BD2


⇒ BD


⇒ = √2 metre


In Δ DBC, DB⊥ BC


⇒ DB2 + BC2 = DC2


⇒ DC = = √3 metre


In Δ CDE, DC⊥ CE


⇒ DC2 + CE2 = DE2


⇒ = 2 metre


In Δ DEF, DE⊥ EF


⇒ DE2 + EF2 = DF2


⇒ DF = = √5 metre….(Ans.)


The area of the square = length of any of its side


= DF2


= (√5)2 = 5 metre2


More from this chapter

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i) What is the area of the square?


ii) What is the altitude of the triangle?


iii) What are the lengths of the other two sides of the triangle shown below?

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