# Ruler and compasses only may be used in this question.

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asked Mar 7

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. ## 1 Answer

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answered Mar 7 by (-2,347 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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