Optimization Examples - Part 5: Maximizing Area of a rectangle inside a semicircle

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Optimization Examples - Part 5: Maximizing Area of a rectangle inside a semicircle
https://youtu.be/0KQk3XYlCpA

In this video I show you can find the maximum area of a rectangle inscribed inside a semicircle using 2 methods: basic calculus and a simpler method using trigonometry.

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# Optimization Examples - Part 5: Maximizing Area of a rectangle inside a semicircle

![Optimization Examples - Part 5.jpg](https://files.peakd.com/file/peakd-hive/mes/EpT9YsY3BiSsqN83cSLywRyX7AgitPtg36CZ1ZQmouLS1WugLJ6GgAM6m1DxEXNTNFq.jpg)

# Example 5

Find the area of the largest rectangle that can be inscribed in a semicircle of radius, r.

## Solution

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8DBnQF65ozybHEZpwRwbenqHCQGR62DsTjMEuLc3HthB3TA8KCaukjdvkGFrV7rRKj.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHbr9ykh997KsKEuxJAMWtmGDUEZJ7oBax9GVev8gh8JE9JXQhmiz23HoVjPvxHQCZv.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tcQixRoaxFC6oAuuY5ogFmq1zTozDMRxBYiD9Wb3mpRdnMy2nDdsbbt38VXCazX5hCv.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/Eo2BpKHNZSBKaSwLWyEeD9RscTMPENzqN2hq7vCraCHtsUvLDMQAmu24SB7bjizo3A3.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8EjqhFwpvmbwRmDuj3GJTKsF7NGZ7L2m7szXum9JffJkNVVuAY8U2uGkMm4NuTJexs.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHbr9ykyPRyy119WmdhFXxsHFwutVwczMEGZTKUMQLXrtmhnDnGNKGHUujssJnvZpqz.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tSzWXZGTLQeHZp9SgBXUhYnxLoT5cANb7uGYJNsxq2jp9NZsWiENPke3U2oo2HnFejz.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/Eo6SGJLzwg6vsG36qD9Sc7KXzPtdd6foRdMYFg38nfozWMPRMGwvbusyR4G4vW1ox84.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tSyz4Yx2vuVyLerSUeddkzGorhpPF1f7Lk5R574uBwtLfxoGEZi9eqi3vpPPb2RJmpL.png)
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