Squaring a Rectangle

Transcript

Squaring a Rectangle Squaring a Rectangle means Given a rectangle, we construct a square of equal area We convert Rectangle ABCD into a square Let’s look at it step-by-step Why this method works? Consider the right angled ∆HKP (highlighted in yellow above). Using the Baudhāyana-Pythagoras theorem we get: 𝐻𝑃^2=𝐻𝐾^2−𝐵𝐻^2 𝑯𝑷^𝟐=((𝒂 + 𝒃)/𝟐)^𝟐−((𝒂 − 𝒃)/𝟐)^𝟐 𝐻𝑃^2=(𝑎^2+2𝑎𝑏+𝑏^2)/4−(𝑎^2−2𝑎𝑏+𝑏^2)/4 𝐻𝑃^2 =4𝑎𝑏/4 𝑯𝑷^𝟐 =𝒂𝒃 Therefore, square HPQS has the same area as rectangle ABCD!