Puzzles
Largest triangle
What is the largest area triangle which has one side of length 4cm and one of length 5cm?
Show answer & extension
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As our shape is a triangle, the 4cm and 5cm sides must be adjacent. Call the angle between them be \(\theta\).
The area of the triangle is \(\frac{1}{2}\times 4\times 5 \times \sin{\theta}\) or \(10\sin{\theta}\). This has a maximum value when \(\theta=90^\circ\), so the largest triangle has and area of 10cm2 and looks like:
Extension
What is the largest area triangle with a perimeter of 12cm?
![](javascript:showlimage("triangle.png"))
![](javascript:showlimage("triangle-biggest.png"))