Two rectangles have the same width, $(x+2)$ cm. Their lengths are $5$ cm and $3$ cm. They are

Question

Two rectangles have the same width, $(x+2)$ cm. Their lengths are $5$ cm and $3$ cm. They are placed side by side along a full edge of length $(x+2)$ cm, forming a larger rectangle of length $8$ cm. Assume $x>0$. Write the combined area as a sum of two products. Then give its expanded and factorised forms. Write and simplify an expression for the perimeter of the larger rectangle. A student adds the perimeters of the two small rectangles. By how much does this exceed the perimeter of the larger rectangle? Explain geometrically. Find the larger rectangle’s area and perimeter when $x=4$.

Accepted Answer

(a) $5(x+2)+3(x+2)=8x+16=8(x+2)\text{ cm}^2$; (b) $2x+20\text{ cm}$; (c) $2(x+2)\text{ cm}$ excess, as the shared internal edge is counted twice; (d) Area $=48\text{ cm}^2$, perimeter $=28\text{ cm}$.

Algebraic Expressions, Identities and Formulae

Algebraic Expressions, Identities and Formulae

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