Construct a rectangle where one of its sides is 5 cm and the length of a diagonal is 7 cm.
To construct a rectangle with one side 5 cm and diagonal 7 cm: Step 1: Draw base CD = 5 cm. Step 2: At point C, construct a perpendicular line (call it l). Step 3: With D as centre, draw a circle (or arc) of radius 7 cm. Step 4: The point where the circle intersects line l is point B. Step 5: From B, draw a perpendicular to BC. Step 6: From D, draw a perpendicular to CD. Step 7: The intersection of these perpendiculars is point A. Rectangle ABCD has side CD = 5 cm and diagonal BD = 7 cm.
Explanation
The chapter explains that to find point B which is 7 cm from D and lies on the perpendicular at C, we use a circle. All points 7 cm from D lie on a circle with centre D and radius 7 cm. The intersection of this circle with the perpendicular line gives point B.
Solution Steps
Step 1: Draw CD = 5 cm.
Step 2: Construct perpendicular at C.
Step 3: Draw circle with centre D, radius 7 cm.
Step 4: Mark intersection point B on the perpendicular.
Step 5: Draw perpendiculars at B and D.
Step 6: Mark intersection point A.
Step 7: Complete rectangle ABCD.