Q. 195.0( 4 Votes )

# Construct a triangle ABC whose perimeter is 12 cm and the angles are in the ratio 2:3:5.

Answer :

Let the angles be 2x, 3x and 5x so that they are in the ratio 2:3:5 now sum of all angles of a triangle is 180°

2x + 3x + 5x = 180°

10x = 180°

x = 18

Thus, angles are 2 × 18 = 36° and 3 × 18 = 54° and 5 × 18 = 90°

Consider 90° and 54° as base angles here

We can use the same method to construct the triangle that we use when perimeter and the base angles are given

Step1: construct a segment XY of length perimeter which is 12 cm

Step2: draw ray at angle 90° from point X and a ray at 54° from point Y

Step3: draw angle bisectors using protractor of X and Y and mark their intersection point as A

Now we have to draw perpendicular bisector of line AX and AY

Step4: take any distance approximately by observation in compass greater than half of XA. Keep the needle of the compass on point A and mark arcs above and below XA and keeping the same distance in compass keep the needle on point X and cut the arcs as shown and join both the intersected arcs. Thus we have drawn the perpendicular bisector of AX. Mark the intersection point of the perpendicular bisector of AX and XY as point B

Step5: similarly draw perpendicular bisector of segment AY and mark the intersection point with XY as C join AB and AC and required ΔABC is ready

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