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 AA1 = A1A2 = A2A3 = A3A4
6. Now join A4B
7. Construct A3P||A4B 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 AB1 = B1B2 = B2B3 = B3B4
11. Join B4C
12. Construct B1Q||B4C 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
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