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Construct a ABC in which AB=5.8 cm, B=60^o and BC+CA=8.4 cm.

Question

Construct a $△ A BC$ in which $A B = 5.8 c m, ∠ B = 6 0^{o}$ and $BC + C A = 8.4 c m$ . Justify your construction.

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Construct a

△ A BC

in which

A B = 5.8 c m, ∠ B = 6 0^{o}

and

BC + C A = 8.4 c m

. Justify your construction.

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Step of Construction:

Construct

A B = 5.8 c m

Construct

∠ A BX = 6 0^{o}

From

BX

, cut the line segment

B D

which is equal to

BC + C A = 8.4

Join the point

A D

Construct a perpendicular bisector of

A D

which meets

B D

at the point

C

In order to obtain the required triangle

A BC

join

A C

Justification:

We know that

C

lies on

A D

which is the perpendicular bisector

So we get

C A = C D

We know that

B D = 8.4 c m

It can be written as

BC + C D = 8.4 c m

So we get

BC + C A = 8.4 c m

Therefore,

△ A BC

is the required triangle.

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Question Text	Construct a $△ A BC$ in which $A B = 5.8 c m, ∠ B = 6 0^{o}$ and $BC + C A = 8.4 c m$ . Justify your construction.
Answer Type	Text solution:1
Upvotes	150

Construct a △ABC in which AB=5.8 cm,∠B=60o and BC+CA=8.4 cm. Justify your construction.

Text solutionVerified

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Construct a $△ A BC$ in which $A B = 5.8 c m, ∠ B = 6 0^{o}$ and $BC + C A = 8.4 c m$ . Justify your construction.