Question

Construct a quadrilateral ABCD in which AB = 4 cm, BC = 4.3 cm, CD = 4.2 cm, and ∠B = ∠C = 90°.

Answer 1

Given:

AB = 4 cm

BC = 4.3 cm

CD = 4.2 cm

And ∠B = ∠C = 90°

Step-wise calculation (Construction):

1. Draw BC = 4.3 cm.

2. At B, construct a right angle to BC (ray BP perpendicular to BC).

On B,P cut off BA = 4 cm and mark point A.

3. At C, construct a right angle to BC (ray CQ perpendicular to BC, on the same side of BC as BA or the opposite side to get the mirror image).

On CQ, cut off CD = 4.2 cm and mark point D.

4. Join A to D to complete the quadrilateral. 

Draw AB and CD already measured and join AD.

Verification

By construction PB ⟂ BC and CQ ⟂ BC.

So, ∠B = ∠C = 90°.

Lengths AB, BC and CD are set to 4 cm, 4.3 cm and 4.2 cm, respectively.

ABCD thus constructed satisfies AB = 4 cm, BC = 4.3 cm, CD = 4.2 cm and ∠B = ∠C = 90°.