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Sam's garden is a rectangle and has a length of 5n and width of n. Shannon's garden has an area of 8n + 21. If the two gardens have equal areas, determine the actual dimensions of Sam's

garden

User Cedrick
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1 Answer

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Given :

Dimensions of Sam's garden is a rectangle and has a length of 5n and width of n.

Shannon's garden has an area of 8n + 21.

To Find :

If the two gardens have equal areas, determine the actual dimensions of Sam's garden.

Solution :

Area of Sam's garden , A = 5n×n = 5n².

So,


5n^2=8n+21\\\\5n^2-8n-21=0\\\\5n^2-15n+7n-21=0\\\\5n(n-3)+7(n-3)=0\\\\n=3\ ,\ n=(-7)/(5)

Since, sides cannot be negative so we will exclude
n=(-7)/(5).

Therefore, the length and width is 15 and 3 units respectively.

Hence, this is the required solution.

User LDJ
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