from a handpicked tutor in LIVE 1-to-1 classes

# Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = 3/4 AB and AQ = 1/4 AC. Join P and Q and measure the length PQ

**Solution:**

Steps of Construction

1. Construct a __line segment__ AB = 5 cm

2. Construct ∠BAZ = 60°

3. With A as centre and 7 cm as __radius__, construct an arc which cuts AZ at the point C

4. Construct a ray AX which makes an angle ∠BAX

5. Let us divide AX into four equal parts AA_{1} = A_{1}A_{2} = A_{2}A_{3} = A_{3}A_{4}

6. Now join A_{4}B

7. Construct A_{3}P||A_{4}B which meets AB at P

8. P is the on AB where AP = 3/4 AB

9. Construct a ray AY which makes an __acute angle__ ∠CAY

10. Now divide AY into four equal parts AB_{1} = B_{1}B_{2} = B_{2}B_{3} = B_{3}B_{4}

11. Join B_{4}C

12. Construct B_{1}Q||B_{4}C which meets AC at Q.

Q is the point on AC where AQ = 1/4 AC

13. Join PQ and measure it

14. Here PQ = 3.25 cm

Therefore, the length of PQ is 3.25 cm.

**✦ Try This: **Two line segments AB and AC include an angle of 30° where AB = 4 cm and AC = 5 cm. Locate points P and Q on AB and AC, respectively such that AP = 1/4 AB and AQ = 3/4 AC. Join P and Q and measure the length PQ.

**☛ Also Check:** NCERT Solutions for Class 10 Maths Chapter 11

**NCERT Exemplar Class 10 Maths Exercise 10.4 Problem 1**

## Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = 3/4 AB and AQ = 1/4 AC. Join P and Q and measure the length PQ

**Summary:**

Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = 3/4 AB and AQ = 1/4 AC. Join P and Q and the length of PQ is 3.25 cm

**☛ Related Questions:**

- Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and ∠ABC = 60°, divide it into triangles BCD . . . .
- Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pai . . . .
- Draw an isosceles triangle ABC in which AB = AC = 6 cm and BC = 5 cm. Construct a triangle PQR simil . . . .

visual curriculum