A square has side length $x$ cm. A rectangle has length $x+3$ cm and width $x-3$ cm, where&nbs

Question

A square has side length $x$ cm. A rectangle has length $x+3$ cm and width $x-3$ cm, where $x>3$. Show that the two shapes have the same perimeter. Find and compare their areas. Generalise your result to a rectangle with sides $x+d$ and $x-d$, where $0<d<x$. Explain what happens to the area as $d$ increases while $x$ stays fixed.

Accepted Answer

(a) Both perimeters $4x$; (b) Rectangle area $x^2-9$, or generally $x^2-d^2$, (c) Smaller by $d^2$.

Algebraic Expressions, Identities and Formulae

Algebraic Expressions, Identities and Formulae

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