A rectangular field has perimeter $300$ metres. It has breadth $x$ metres and length $y$ metre

Question

A rectangular field has perimeter $300$ metres. It has breadth $x$ metres and length $y$ metres. Express $y$ in terms of $x$. Show that the total area, $A$ m$^2$, of the field is given by $A=5625-{{\left( x-75 \right)}^{2}}$. Determine whether $A$ is a maximum or a minimum. Hence, state this value of $A$ and the corresponding value of $x$.

Accepted Answer

(a) $y = 150 - x$ (b) $A = 5625 - (x - 75)^2$ (c) $A$ is a maximum; Maximum value of $A=5625$ m$^2$; Value of $x = 75$ m

Quadratic Functions, Equations and Inequalities - Completing the Square and Vertex Form

Quadratic Functions, Equations and Inequalities - Completing the Square and Vertex Form

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