Categories

# Length of side of Triangle | PRMO II 2019 | Question 28

Try this beautiful problem from the Pre-RMO, 2017, Question 23, based on Solving Equation. You may use sequential hints to solve the problem.

Try this beautiful problem from the Pre-RMO II, 2019, Question 28, based on Length of side of triangle.

## Length of side of triangle – Problem 28

In a triangle ABC, it is known that $$\angle$$A=100$$^\circ$$ and AB=AC. The internal angle bisector BD has length 20 units. Find the length of BC to the nearest integer, given that sin 10$$^\circ$$=0.174.

• is 107
• is 27
• is 840
• cannot be determined from the given information

### Key Concepts

Equation

Algebra

Integers

But try the problem first…

Source

PRMO II, 2019, Question 28

Higher Algebra by Hall and Knight

## Try with Hints

First hint

given, BD=20 units

$$\angle$$A=100$$^\circ$$

AB=AC

In $$\Delta$$ABD

$$\frac{BD}{sinA}=\frac{AD}{sin20^\circ}$$

or, $$\frac{BD}{sin100^\circ}=\frac{AD}{sin20^\circ}$$

or, 20=$$\frac{AD}{2sin10^\circ}$$ or, AD=40sin10$$^\circ$$=6.96

Second Hint

In $$\Delta$$BDC

$$\frac{BD}{sin40^\circ}=\frac{BC}{sin120^\circ}=\frac{CD}{sin20^\circ}$$

or, CD=$$\frac{20}{2cos20^\circ}$$=$$\frac{20}{2 \times 0.9394}$$=10.65

Final Step

since BD is angle bisector

$$\frac{BC}{AB}=\frac{CD}{AD}$$

or, BC=$$\frac{AB \times CD}{AD}$$=$$\frac{17.6 \times 10.65}{6.96}$$

=26.98=27.

## Subscribe to Cheenta at Youtube

This site uses Akismet to reduce spam. Learn how your comment data is processed.