Question

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Q). contruct a triangle ABC in which BC = 7 cm . Angle B 75° and AB + AC = 13 cm .

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Answer 1

Solution :-

Steps of construction :-

$\longrightarrow$ Draw a rough sketch of ΔABC and mark the given measurements as usual.

Analysis :

As we have AB + AC = 13 cm, extend BA up to D such that BD = 13 cm

Therefore BD = AB + AD = 13 cm

Given : AB + AC = 13 cm

⇒ AB + AD = AB + AC

⇒ AD = AC

As A is equidistant from C and D, draw a perpendicular bisector of CD to locate A on BD.

$\longrightarrow$ Draw the base BC = 5 cm and construct ∠CBX = 75° at B

$\longrightarrow$ With B as centre and radius 13 cm ( AB + AC = 13 cm ) draw an arc on BX to intersect at D.

$\longrightarrow$ Join CD and draw a perpendicular bisector of CD to meet BD at A.

$\longrightarrow$ Join AC to get the required triangle ABC.

( Refer the attachment for construction )