In a △ABC, 2∠A = 3∠B and ∠C = 100°. The correct ascending order of sides of the triangle is : 1. AC BC AB 2. BC AC AB 3. AB AC AB 4. BC AB AC

Given, 2∠A = 3∠B ⇒ ∠A : ∠B = 3 : 2 ⇒ ∠A = 3x° and ∠B = 2x° In △ABC, By angle sum property of triangle, ⇒ ∠A + ∠B + ∠C = 180° ⇒ 3x° + 2x° + 100° = 180° ⇒ 5x° = 180° - 100° ⇒ 5x° = 80° ⇒ x° = ⇒ x° = 16° ⇒ ∠A = 3x° = 3 × 16° = 48° ⇒ ∠B = 2x° = 2 × 16° = 32° We know that, The longest side of a triangle has the largest angle opposite to it. Since, C is the largest angle, thus AB is longest side of the triangle. The shortest side of a triangle has the smallest angle opposite to it. Since, B is the smallest angle, thus AC is smallest side of the triangle. ∴ AC BC AB. Hence, option 1 is the correct option.

In a △ABC, ∠A = 40° and ∠B = 60°. The longest side of the triangle is:
AB
BC
CA
None of these

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In a △ABC, AB = 6 cm, BC = 7 cm and CA = 8 cm. The smallest angle of the triangle is :
∠A
∠B
∠C
None of these

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The angles of a triangle are 5(x - 4)°, (4x + 5)° and (x + 25)°, then the value of x is :
17
18
19
21

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In △ABC, AB > AC and D is any point on BC, then, AB is :
< DC
< AD
= BC
> AD

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Mathematics

In a △ABC, 2∠A = 3∠B and ∠C = 100°. The correct ascending order of sides of the triangle is :
AC < BC < AB
BC < AC < AB
AB < AC < AB
BC < AB < AC

Triangles

Related Questions

In a △ABC, ∠A = 40° and ∠B = 60°. The longest side of the triangle is:
AB
BC
CA
None of these

In a △ABC, AB = 6 cm, BC = 7 cm and CA = 8 cm. The smallest angle of the triangle is :
∠A
∠B
∠C
None of these

The angles of a triangle are 5(x - 4)°, (4x + 5)° and (x + 25)°, then the value of x is :
17
18
19
21

In △ABC, AB > AC and D is any point on BC, then, AB is :
< DC
< AD
= BC
> AD

Mathematics

In a △ABC, 2∠A = 3∠B and ∠C = 100°. The correct ascending order of sides of the triangle is :AC < BC < ABBC < AC < ABAB < AC < ABBC < AB < AC

Triangles

Related Questions

In a △ABC, ∠A = 40° and ∠B = 60°. The longest side of the triangle is:ABBCCANone of these

In a △ABC, AB = 6 cm, BC = 7 cm and CA = 8 cm. The smallest angle of the triangle is :∠A∠B∠CNone of these

The angles of a triangle are 5(x - 4)°, (4x + 5)° and (x + 25)°, then the value of x is :17181921

In △ABC, AB > AC and D is any point on BC, then, AB is :< DC< AD= BC> AD

In a △ABC, 2∠A = 3∠B and ∠C = 100°. The correct ascending order of sides of the triangle is :
AC < BC < AB
BC < AC < AB
AB < AC < AB
BC < AB < AC

In a △ABC, ∠A = 40° and ∠B = 60°. The longest side of the triangle is:
AB
BC
CA
None of these

In a △ABC, AB = 6 cm, BC = 7 cm and CA = 8 cm. The smallest angle of the triangle is :
∠A
∠B
∠C
None of these

The angles of a triangle are 5(x - 4)°, (4x + 5)° and (x + 25)°, then the value of x is :
17
18
19
21

In △ABC, AB > AC and D is any point on BC, then, AB is :
< DC
< AD
= BC
> AD