Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.

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asked Oct 2, 2018 in Class IX Maths by aditya23 (-2,140 points)

Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.

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1 Answer

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answered Oct 2, 2018 by priya12 (-12,564 points)

Steps of Construction

 (i) Draw BC = 12 cm. 

(ii) Construct ÐCBY = 90°. 

(iii) From ray BY, cut-off line segment BD = 18 cm. 

(iv) Join CD. 

(v) Draw the perpendicular bisector of CD intersecting BD at A. 

(vi) Join AC to obtain the required  △ABC.

Justification

Since A lies on the perpendicular bisector of CD.

Therefore, AD = AC 

Now,    BD = BA + AD 

⇒    BD = AB + AC

 Hence,  △ABC is the required triangle.

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