MediumMathematicsHigh School (9–10)GeneralAlgebra › Quadratic EquationsNumericalword problem

A rectangular hall must have a perimeter of 52 m.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A rectangular hall must have a perimeter of $52\ \text{m}$ . Can its floor area be $180\ \text{m}^2$ ? Can it be $168\ \text{m}^2$ ? For any area that is possible, find the sides.

Need a reminder? The key ideaShow

The discriminant of $ax^2 + bx + c = 0$ is $D = b^2 - 4ac$ . If $D > 0$ there are two distinct real roots, if $D = 0$ two equal real roots, $x = -\dfrac{b}{2a}$ , and if $D < 0$ no real roots.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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A rectangular hall must have a perimeter of 52 m.

The worked solution

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