Question

State whether the triangle is possible to construct if
(a) In ΔABC, m∠A = 80°, m∠B = 60°, AB = 5.5 cm
(b) In ΔPQR, PQ = 5 cm, QR = 3 cm, PR = 8.8 cm​

Solution:
(a) m∠A = 80°, m∠B = 60°
m∠A + m∠B = 80° + 60° = 140° < 180°
So, ΔABC can be possible to construct.
(b) PQ = 5 cm, QR = 3 cm, PR = 8.8 cm
PQ + QR = 5 cm + 3 cm = 8 cm < 8.8 cm
or PQ + QR < PR
So, the ΔPQR can not be constructed.

Answer 1

Answer:

(a) m∠A = 80°, m∠B = 60°

m∠A + m∠B = 80° + 60° = 140° < 180°

So, ΔABC can be possible to construct.

(b) PQ = 5 cm, QR = 3 cm, PR = 8.8 cm

PQ + QR = 5 cm + 3 cm = 8 cm < 8.8 cm

or PQ + QR < PR

So, the ΔPQR can not be constructed.

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Answer 2

• a) Triangle is possible to construct .
• B) Triangle is not possible to construct .

To Find :- State whether the triangle is possible to construct if :-

(a) In ΔABC, m∠A = 80°, m∠B = 60°, AB = 5.5 cm

(b) In ΔPQR, PQ = 5 cm, QR = 3 cm, PR = 8.8 cm

Concept used :-

• When two angles and a side is given, only one triangle can be formed .
• Sum of all three angles of a triangle is equal to 180° .
• Sum of length of any two sides of a triangle is always greater than the third side .
• Difference between length of any two sides of a triangle is always smaller than the third side .

Solution :-

a) In ΔABC, m∠A = 80°, m∠B = 60°, AB = 5.5 cm

→ m∠A + m∠B + m∠C = 180° { Angle sum property }

→ 80° + 60° + m∠C = 180°

→ 140° + m∠C = 180°

→ m∠C = 180° - 140°

→ m∠C = 40°

Also sum of given two angles of triangle is less than 180° . Therefore, given triangle is possible with one solution .

Steps of construction :-

• Draw a line segment AB of length 5.5 cm .
• From point A draw an angle of 80° with the help of protractor .
• From point B draw an angle of 80° with the help of protractor .
• Let both ray from A and B meets at point C .
• ∆ABC is the required triangle .

(b) In ΔPQR, PQ = 5 cm, QR = 3 cm, PR = 8.8 cm

checking if sum of length of any two sides of a triangle is greater than the third side :-

→ PQ + QR > PR => 5 + 3 > 8.8 => 8 < 8.8

since sum of length of PQ and QR is less than third side PR, given triangle is not possible .

→ PQ + PR > QR => 5 + 8.8 > 3 => 13.8 > 3

→ QR + PR > PQ => 3 + 8.8 > 5 => 11.8 > 5

checking if difference between length of any two sides of a triangle is smaller than the third side :-

→ PQ - QR < PR => 5 - 3 < 8.8 => 2 < 8.8

→ PR - QR < PQ => 8.8 - 3 < 5 => 5.8 > 5

→ PR - PQ < QR => 8.8 - 5 < 3 => 3.8 > 3

As we can see that, difference between length of PR and QR is greater than PQ and difference between length of PR and PQ is greater than QR, therefore, given triangle is not possible .

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