Construct a ∆PQR such that QR = 6.5 cm, ∠P = 60° and the altitude from P to QR is of length 4.5 cm.

10th Standard Maths Quarterly Exam Sep 2024 Answer Key | Brindhavan HR SEC School

b) Construct a ∆PQR such that QR = 6.5 cm, ∠P = 60° and the altitude from P to QR is of length 4.5 cm.

Answer:

Triangle Construction Rough Diagram Triangle Construction Real Diagram

Construction:

  1. Draw a line segment QR = 5 cm.
  2. At Q, draw QE such that ∠RQE = 30°.
  3. At Q, draw QF such that ∠EQF = 90°.
  4. Draw the perpendicular bisector XY to QR, which intersects QF at O and QR at G.
  5. With O as centre and OQ as radius, draw a circle.
  6. The major arc QKR contains the angle 30°.
  7. From G, mark a point H on XY such that GH = 4.2 cm.
  8. Draw a line AB through H parallel to QR. This line intersects the circle at P and P'.
  9. Join QP and RP. Then ∆PQR is the required triangle.
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