$A B = 5 c m, B C = 4 c m$ and $A C = 6 c m$ . State, with reason, whether it is possible to draw $Δ A B C$ or not.

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Solution

$\begin{matrix} Y e s i t i s p o s s i b l e t o d r a w t h e t r i a n g l e . b e c a u s e w h e n s u m o f 2 s i d e s i s m o r e t h a n t h i r e d s i d e, w e c a n d r a w t h e t r i a n g l e S o s u m o f 2 s i d e s w i l l b e 5 + 4 > 6 [C r i t e r i a m e t] 4 + 6 > 5 [C r i t e r i a m e t] 6 + 5 > 4 [C r i t e r i a m e t] H e n c e, i t i s p o s s i b l e t o d r a w t h e t r i a n g l e . \end{matrix}$

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Similar questions

$In each of the following cases,given reasons to show that the construction of Δ A B C i s n o t p o s s i b l e : (i) A B = 6 c m, ∠ A = 40^{\circ} a n d (B C + A C) = 5.58 c m (i i) A B = 7 c m, ∠ A = 50^{\circ} a n d (B C - A C) = 8 c m (i i i) B C = 5 c m, ∠ B = 80^{\circ}, ∠ C = 50^{\circ}, a n d ∠ A = 60^{\circ} (i v) A B = 4 c m, B C = 3 c m, a n d A C = 7 c m .$

Question 73

State whether the statement is True or False.

In $Δ A B C$ , AB = 3.5 cm, AC = 5 cm, BC = 6 cm and in $Δ P Q R$ , PR = 3.5 cm, PQ = 5 cm, RQ = 6 cm. Then, $Δ A B C ≅ Δ P Q R$

Q. In

Δ

ABC and

Δ

PQR, AB = 4 cm, BC = 5 cm, AC = 6 cm and PQ = 4 cm, QR = 5 cm, PR = 6 cm, then

There is a unique quadrilateral ABCD possible with AB = 4 cm, BC = 6 cm, AC = 7 cm, CD = 5 cm and BD = 8 cm. State True or False.

Q. Draw a ΔABC in which BC = 6 cm, AB = 4 cm and AC = 5 cm. Draw a triangle similar to ΔABC with its sides equal to (3/4)^th of the corresponding sides of ΔABC.

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AB=5 cm, BC=4 cm and AC=6 cm. State, with reason, whether it is possible to draw ΔABC or not.

Yesitispossibletodrawthetriangle.becausewhensumof2sidesismorethanthiredside,wecandrawthetriangleSosumof2sideswillbe5+4>6[Criteriamet]4+6>5[Criteriamet]6+5>4[Criteriamet]Hence,itispossibletodrawthetriangle.

$A B = 5 c m, B C = 4 c m$ and $A C = 6 c m$ . State, with reason, whether it is possible to draw $Δ A B C$ or not.