A rectangular courtyard measures $20\text{ m}$ by $12\text{ m}$. A path of uniform width \(x\tex

Question

A rectangular courtyard measures $20\text{ m}$ by $12\text{ m}$. A path of uniform width $x\text{ m}$ runs inside the courtyard along all four edges. The uncovered rectangular region has area $128\text{ m}^2$. Write down the length and width of the uncovered region in terms of $x$.[1] Form an equation and show that it simplifies to $x^2-16x+28=0$.[2] Solve the equation and find the width of the path. Explain why one positive root must be rejected.[3]

Accepted Answer

(a) $(20-2x)\text{ m}$, $(12-2x)\text{ m}$ (b) $x^2-16x+28=0$ (shown) (c) $2\text{ m}$; $x=14$ violates $0<x<6$.

Geometric restrictions

Geometric restrictions

Solution:

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