Q. 54.3( 271 Votes )

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

Answer :

Given base BC = 12 cm

∠ B = 90°

And AB (other side)+ AC (hypotenuse)= 18 cms.

*Steps of construction*:

i. Draw a base line BC of 12 cms.

ii. Construct ∠ B = 90°.

a. With B as centre and with any radius, draw another arc cutting the line BC.

b. With D as centre and with the same radius, draw an arc cutting the first arc (drawn in step b) at point E.

c. With E as centre and with the same radius, draw another arc cutting the first arc (drawn in step b) at point F.

d. With E and F as centers, and with a radius more than half the length of EF, draw two arcs intersecting at point G.

e. Join points B and G. The angle formed by GBC is 90°. i.e.

∠ GBC = 90°.

iii. With B as centre draw an arc with length 18 cms ( = AB + AC given), such that it intersects ray BG at H.

iv. Join CH and we draw a perpendicular bisector for CH.

a. By drawing arcs on both sides of the line CH, with C and H as centers and with same lengths. These arcs intersect at I and J on either side of line CH.

v. The perpendicular bisector for CH will intersect the ray BH at point A. Join AC.

Thus the formed triangle ABC is the required triangle with right angle formed at B.

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