In ∆ ABC, AB = 2.5 cm and BC = 6 cm. Then, the length of AC cannot be
(a) 3.4 cm
(b) 4 cm
(c) 3.8 cm
(d) 3.6 cm

Open in App

Solution

(a) 3.4 cm
In triangle ABC, AB = 2.5 cm and BC = 6 cm.
The length of a side must be less than the sum of the other two sides.
Let the side AC be x cm.
i.e., $x < 2.5 + 6 \Rightarrow x < 8.5$
In addition, the length of a side must be greater then the difference between the other two sides.
i.e., $x > 6 - 2.5 \Rightarrow x > 3.5$
Hence, the limits for the value of x is $3.5 < x < 8.5$ .
Thus, the length of AC cannot be 3.4 cm

Suggest Corrections

Similar questions

△

ABC is constructed such that AB = 3 cm, BC = 5 cm and

∠

A = 90

^{\circ}

. Then the length of side AC is

Q. Construct

∆

ABC, such that BC = 6 cm,

∠

ABC =

100^{°}

and AC

-

AB = 2.5cm.

Q. Construct

Δ A B C

, such that

B C = 6 c m

∠ A B C = 100^{0}

and

A C - A B = 2.5 c m

Q. Construct

△ A B C

such that

A B = 2.5 c m, B C = 6 c m

and

A C = 6.5 c m

. Measure

∠ B

In a $Δ A B C$ , AD is the bisector of $∠ A$ , meeting side BC at D.
(i) If BD= 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD= 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB= 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB =10 cm, AC =14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AD= 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
(viii) If AB =10 cm, AC = 6 cm and BC = 12 cm, find BD and DC

Join BYJU'S Learning Program

In ∆ ABC, AB = 2.5 cm and BC = 6 cm. Then, the length of AC cannot be (a) 3.4 cm (b) 4 cm (c) 3.8 cm (d) 3.6 cm

In ∆ ABC, AB = 2.5 cm and BC = 6 cm. Then, the length of AC cannot be
(a) 3.4 cm
(b) 4 cm
(c) 3.8 cm
(d) 3.6 cm