Construct a rectangle one of whose sides is 4 cm and the diagonal is of length 8 cm.
To construct a rectangle with one side 4 cm and diagonal 8 cm: Step 1: Draw base CD = 4 cm. Step 2: At point C, construct a perpendicular line. Step 3: With D as centre, draw a circle of radius 8 cm. Step 4: The intersection of the circle with the perpendicular line gives point B. Step 5: From B, draw a perpendicular to BC. Step 6: From D, draw a perpendicular to CD. Step 7: The intersection is point A. Rectangle ABCD has side CD = 4 cm and diagonal = 8 cm.
Explanation
This uses the same method as the 5 cm side, 7 cm diagonal construction. The circle technique locates the vertex that is at the specified diagonal distance from the opposite corner.
Solution Steps
Step 1: Draw CD = 4 cm.
Step 2: Construct perpendicular at C.
Step 3: Draw circle with centre D, radius 8 cm.
Step 4: Mark intersection B on perpendicular.
Step 5: Draw perpendiculars at B and D.
Step 6: Mark intersection A.
Step 7: Complete rectangle.