Ruler and compasses only may be used in this question.

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asked Mar 7 in Class X Maths by priya12 (-11,688 points)

Ruler and compasses only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.

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1 Answer

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answered Mar 7 by muskan15 (-2,549 points)

Steps of construction:

(i) (1) Mark a horizontal line XY on your paper and take BC = 6 cm on it.

(2) Construct ∠ABC = 60 ̊ with arm  AB = 9 cm.

(3) Join A and C to get the required  ΔABC.

(iii) (1) Draw AD ⊥ BC.

(2) Construct a line X’Y’, perpendicular to AD, parallel to XY and passing through A.

(3) X’Y’ is the required locus of the vertices of  Δ’s with base BC and area to ΔABC.

[∵  Δ’s having same base and height an equal in area ]

(iii) (1) Draw right bisector PQ of BC, meeting X’Y; in Q.

(2) Then Q is the point such that ΔQBC  is an isosceles triangle and area (ΔQBC) = area(ΔABC).

(iv) On measuring, we find CQ = 8.4 cm.

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