Question

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

Answer 1

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,

$5n^2=8n+21\\\\5n^2-8n-21=0\\\\5n^2-15n+7n-21=0\\\\5n(n-3)+7(n-3)=0\\\\n=3\ ,\ n=\dfrac{-7}{5}$

Since, sides cannot be negative so we will exclude $n=\dfrac{-7}{5}$.

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

Hence, this is the required solution.